Very complicated questions, but I will try to answer the 35mm lens question.

"Does a 35mm lens mean we should ideally stand 35mms away from a statue for the best shot?" No.

The physical length of a lens often is different from its optical length.

For simple lenses, a lens needs to be physically at its focal length to be focused at infinity if it was a 90mm lens that would be at 90mm from the sensor. At 90mm it would be focusing whats at 'infinity' on the surface of the sensor. kind of like focusing a projector on a screen but in reverse. If the lens is nearer than its focal length then its focusing beyond infinity and the image projected on the sensor is blurry. To focus on something nearer than infinity the lens needs to move further away from the sensor. This isn't a straight line relationship but a logarithmic one.

To focus at 10x the focal length the distance is 1.1 x focal length for a 90mm lens to focus at 900mm that would be 99mm
to focus at 100x the focal length the distance is 1.01 x focal length for the 90mm lens to focus at 9000mm it would be 90.9 mm
to focus at 1000x the focal length the distance is 1.001 x focal length for the 90mm lens to focus at 90,000mm it would be 90.09mm

converting those real-world distances
900mm = 90cm or 0.9meters about 3 feet
9000mm = 9 meters about 30 feet
90,000mm = 90 meters about 300 feet
Basically, infinity is when the lens is so close to being positioned at its focal length you just can't move it that precisely.
closer than about 10x and the distance the lens has to move away from the sensor increases rapidly. e.g focusing at 180mm would require the 90mm lens to move out by 90mm which is beyond what is practical for most helicoids. You can use extension tubes between the lens and the camera to focus in closer than normal.

Optics can make these physical distances completely wrong, I avoided the 35mm lens in this explanation because the registration distance of an SLR (depending on brand) tends to be 44 - 47mm so 35mm is inside the lens mount, so a 35mm lens is not a simple lens :)

ok, you should now have a handle on
"beyond infinity" lens closer than its focal length to the sensor
"infinity" when the lens is at its focal length or so close it makes no difference
and what happens when you want to focus nearer than infinity. Unless a lens is a macro lens (designed to focus extremely close up) 10x focal length is a good ballpark figure for minimum focus distance.

Shorter lenses focus closer than longer lenses and infinity is nearer for shorter lenses than longer lenses. The depth of field on a short lens will make most of what you see in front of the camera in focus and longer lenses will have a narrower depth of field. Field of view the width and height of what you see also changes between wide angle lenses which give a wide field of view too long telephoto lenses which give a narrow field of view. Because your sensor is a fixed size wide angle lenses give the effect of being further away than telephoto lenses.

Different sensor sizes take a different crop of whats projected on the back wall of the camera for a full frame enlarging that image by about a factor of 7x would give a photo about 8 by 10 for a crop sensor camera enlarge by about 10x for the same size photo and 49x for an iPhone sensor.

So a given focal length might be wide angle, normal, or telephoto depending on the sensor size. You need to know the system you are using to be able to be able to say if a focal length is going to be a wide angle, a normal or a telephoto lens on that camera.

When most people were using 35mm cameras around 50mm was considered a normal lens (giving an image with the same view as your eye) there is a more technical definition but we don't care :) a 28mm would be considered wide and anything longer than 50mm telephoto (people will argue that definition too). You could kinda say the 28mm lens was about half the 50mm lens focal lens and would be similar to being twice the distance of your subject and a 100mm lens a bit like being twice as close.

With modern digital sensors, the sensor size changes those values an aps-c camera you can multiply the focal length by 1.5 to get an approximation of the 35mm view so a 50mm looks like 75mm (a bit telephoto) the 28mm looks like 42mm (pretty close to normal)

If you only know your own camera system then you will figure it out, but crop factors are useful comparing against different sensor sizes.

A focal length is a focal length of any camera system even though the image you can capture is vastly different across systems.

10x focal length is a fair rule of thumb for the minimum focus distance so expect to be able to focus as close as 50cm with a 50mm lens and 2 meters with a 200mm lens.

Zoom lenses are a compromise generally a smaller zoom lens range will give better IQ than a wider zoom range, better quality lenses should do better than cheaper lenses but you pay for that :) bigger sensors require larger diameter lens elements than smaller sensors in order to make a large enough image circle to cover the sensor (this also makes them more expensive).

A fast lens (say 2.8 or better) lets in more light than a more consumer orientated lens like an f4 lens it helps focus faster and gives faster shutter speeds you pay for that too. There's also a rule of thumb that says stopping 2 stops down from wide open gives the best image quality another advantage to a fast lens.

It would be nice to be able to afford these fast lenses but you can still get great results with more affordable lenses. It's your eye that makes the composition and the compelling photograph. It's the photographer that makes the biggest difference.

The longer the focal length of a lens the more sensitive it is to movement, which means raising shutter speed. This means less light reaches the sensor so you need to increase aperture and raise the iso sensitivity of the camera. There is a practical limit to this which may make for lousy photos, a shorter lens will capture more of the scene but less of the detail but it will be able to use lower shutter speed. It's a compromise.

Hope this helps some.

What does a lens's focal distance tell me to do? In other words, will knowing the focal length of a lens determine my optimal distance in yardage or mileage from a subject? Or is it a complex calculation of factors within the lens itself? I know that there is some relationship between the physical length of a lens and the physical distance it can "reach," so I do know to select a longer lens for air shows and wildlife than for capturing a house pet.

However there are so many different lenses to choose from, and while all are identified by their focal length in millimeters as well as by their aperture ranges, yet some might be 200-400, or 100-300, or 100-400mms for example, so how do those similar ranges advise us to choose among them. Is there a ratio, a formula, for that relationship that guides us in choosing the appropriate lens for a given situation, or are other parameters more relevant? Does a 35mm lens mean we should ideally stand 35mms away from a statue for the best shot? Should we know the distance to a river's shore from a river cruise ship in order to select a lens to shoot the scenery we pass? What about when shooting birds in flight -- does the number relate to our distance to them on the ground or from the ground to where the birds are in the sky?
Maybe there is an obvious explanation that I'm missing, but I would love to know what it is! So thanks in advance for enlightening me :-)

What does a lens's focal distance tell me to do? In other words, will knowing the focal length of a lens determine my optimal distance in yardage or mileage from a subject? Or is it a complex calculation of factors within the lens itself? I know that there is some relationship between the physical length of a lens and the physical distance it can "reach," so I do know to select a longer lens for air shows and wildlife than for capturing a house pet.

However there are so many different lenses to choose from, and while all are identified by their focal length in millimeters as well as by their aperture ranges, yet some might be 200-400, or 100-300, or 100-400mms for example, so how do those similar ranges advise us to choose among them. Is there a ratio, a formula, for that relationship that guides us in choosing the appropriate lens for a given situation, or are other parameters more relevant? Does a 35mm lens mean we should ideally stand 35mms away from a statue for the best shot? Should we know the distance to a river's shore from a river cruise ship in order to select a lens to shoot the scenery we pass? What about when shooting birds in flight -- does the number relate to our distance to them on the ground or from the ground to where the birds are in the sky?
Maybe there is an obvious explanation that I'm missing, but I would love to know what it is! So thanks in advance for enlightening me :-)