With the camera you have, it is more than enough. I have been there more than dozen times, never needed a zoom lens. Unless you want to take picture of the falls of the Canadian side from the bridge or the falls and the bridge from the falls. Like it has been mentioned, please be careful about getting your camera wet if you take journey either in the boat or journey behind the Niagara falls. If you walk along the side of the fence, you will reach the steps before you get down for the boat trip. That would also be a good location to take photos. Look out of rainbows.
And about pyramids, they are huge, you have to be at a distance to get the photo OR a wide angle lens. I would suggest that, with you camera, start walking from a distance and you will be able to take good photos. If you land just near the pyramid, it would be difficult to cover the entire pyramid(s). Again, the photos at sunset or sunrise would be very wonderful as it brings out the colors of the pyramid and great shadows as well.

No need of any prime lens. You could just take great shots with the specified camera and the lens. Photos please.....

Sometimes, if you just tilt camera either left or right / up or down, you could avoid some of the bright reflection of the sun light from the leaves in the background. If that doesn't change may be positioning yourself in a different angle. It is about how light flows through your lens and that's how the AUTO mode sets the rest of the settings. I guess I have answered your doubt. Please let me know if you need any clarifications. Thank you

By looking at the photos, the second one looks better than the other two. And about the over exposed photos, the AUTO settings of your camera metered the scene and increased ISO, the sensitivity, which was not needed. That is one of the reasons that you don't see the colors properly. Even with the AUTO settings, one way you could have improved photos, either by changing the direction of your camera or by using polarizing lens.

Please post some photos for analyzing. Besides that, let us know about the mode you were shooting. Was it in AUTO or some other mode. You could try increasing shutter speed, but that might not be the case at all. Question is how blurry are they?

As wisner says, you can try one of those. Wait for different time of the day or month or year, assuming that you get good lighting for the falls. Anytime you feel like the sky is blown out, it is best not to include that as part of the composition and still keep the photograph interesting.
Some ideas that you can try,
You can take at least 3 photos with different exposure and use the same to create an HDR image.
You could try using CPL (polarizer)filter.
You could try using graduated ND (neutral density)filter, which will give exactly the result you are expecting for this situation.

In the above photos, I am assuming that the camera is in either spot or center weighted metering mode. I think it would have been little darker (especially the bottom part), if it would have been Matrix metering.
Please also try different modes and let us know if you have any further questions.

I think it is because of the combination of two filters. Never happened to me. Even just using ND filter, I have always got good color. I have always used it for longer exposure. It is always good to have at least ND 2, 4, 6, 8. Depending on the condition and how long you need the exposure to be, you can use one of those.
You can also try only with CPL and the setting f22, ISO 100 with lower shutter speed of about 1/4 or 1/2 or even 1 second. You should be able to get a good result.

By setting the camera to M-manual position, Please try with shutter speed starting from 1/500. Depending on the light, try to increase the ISO. This should give you the possibility of higher shutter speeds. Try these options, which will come in handy for the next session.

In my opinion, and looking at the picture, you didn't need ISO 200 and the photo is out of focus ( as you mentioned of windy weather). Keeping that in mind, i would think 1/250 is still low. ISO 100 and high shutter speed (for the movement) would work. To bring out the color(s), i would say, may be you can try polarize lens. With the lens you have mentioned, if you had zoomed quite well and with the hand held you might get the vibration. Reduce the zoom and you can give that a try. Please try different options and let us know.

In couple of instances i have taken martial art photos. First thing I am assuming is that the camera is set to manual and nothing else. Usually for this type of situations, after all the settings (Aperture, ISO, Shutter Speed, Metering) done with the camera, try to see where would the subject(s) land up. Because that defines the final focus for me. Once that is done, you would know exactly where to focus. Once that is set, change the auto focus to manual focus. Try some shots so that you know your focus is where it is supposed to be. Let me know if you need further info. Thanks

As "Marionsho" said, you could have used CPL (Polarizing Filter) to reduce the glare and to get a good color for that.
What I would have done is, after studying the subject, i would have changed the direction of the car a little bit so that the sun rays are not coming towards the camera. It is just the way of directing the light somewhere else or you could have tried moving yourself little left of right so that you could reduce the glare as much as possible. Even without the CPL filter, try different positions. You might see the difference.

One question. Just to avoid the dark are shadowy areas, did you take all the photos with the same exposure and in manual settings including ISO. If the camera meters with auto settings you would usually fine these effects when you stitch them. For now, if the photos are in RAW, you might want to edit them in Photoshop with the same settings and adjust the exposure or brightness/contrast to get the effect. Please let us know.

I think the problem is with the metering itself. Both the photos have different centers (assuming that both are center weighted). But the camera seems to have metered based on that and that's how you have the sky blown out in the second photo.

To get it perfect, you can do 2 things. Using RAW file you can edit the shadows and try to make it perfect. OR you can take 2 photos of different exposures and you would have to combine them in Photoshop to get it perfect.

In landscape photography, it is better to have something in the foreground to enhance the look and to make eyes follow the flow. The foreground can either be clear or blurred with different DOF

The lower the DOF (Depth of Field) the more blurrier the objects look which are out of focus.

f/4.5 is very less DOF, it might make it blurrier but you might still see the white spots. In my opinion, i would say keep the DOF between 11 - 16, which will eliminate blurriness and the picture should be clearer. Let us know if you get one of those photos again