Depends of how you define better. In my experience a good smartphone camera can be used for pretty good close up or macro ish photography because you can place it very close to the subject and still get a lot of it in focus. This is probably the strongest photographic advantage of a smartphone. And this is all due to the small sensor in a smartphone.
I suggest you give it a try just to experiment and see what you get, it might be a surprisingly good result.

I have a Nikon 1 J2 and J5. Like them both. The J5 delivers better colors. If you need a compact gear nothing will beat a Nikon 1 and the glass of your choice. I often travel with the J5 and the kit lens in my jacket pocket and another lens in another pocket. No need for a camera bag for a body and 2-3 lenses if you have a Nikon 1 gear. If you are tight on budget go with the J3, if you can afford more get the J5.

What you loose in image quality depends on what kind of image quality is important for you. If you go for a 18-400 Tamron or other superzoom lenses you will loose the soft foregrounds/backrounds you can get when using prime lenses at wide open apertures. And you would loose some ability to take pics in low light. But many recent zooms will deliver sharp images at most of the zoom range so if that is what you need then it is an easy choice. I guess you are not thinking much about night or very low light photography so the zoom lenses should be fine in that regard as well.

No. You are just cropping your picture in camera. No affect on the lens.

Yes, the 1" sensor is a 2.7X crop sensor.

I started with a Konica in the 80's. Then switched to Nikon and have been shooting Nikon film cameras and D80, D200, D3200, D600 until I decided to try Sony A7r about 3 years ago. For me it is by far the best fit camera for my needs. Would get either the Sony A7iii or A7riii if I was switching today.

You will need your widest lens, so if you were to take only one lens for the Nikon it should be the 16-35 lens. If you are mainly in those cities that is about all you need. The Fuji will be of little use with the 35 mm lens.

All about the D7200 focus point and focus system is in the manual, please download it and read it. http://downloadcenter.nikonimglib.com/en/products/197/D7200.html

Yes, it was the smallest 35 mm camera. At least until the Minox 35 came along. I think it is a tad smaller. Would be fun to check the size since I own both the Minox and the Rollei.

A lot of this exakt kit is sold used for $5-600 on Ebay. Some are priced at $8-900. Your camera will fit somwhere in this range.

You should look at the new Sony A7iii. It is great for shooting your kids in sports and excellent owerall camera. The price is $2000. You could get a 70-200 lens or 100-400 to get pics of your kids and some landscape shots and choose from a whole bunch of other lenses for the close up shots and landscapes. One of the advantages of this camera is that you can just as well use good old manual glass as modern autofocus glass to use in landscape photography and for the close ups. You could get macro lens for either full frame or Aps-c as you will never need all the resolution of the full frame sensor for your product photos. So you can buy this body and be all set with investment from around $4500 in camera and good glass for your needs without trading in or selling your Nikon gear. Maybe you can get around $1000 by selling that directly on ebay or locally, less if you trade it.

Maybe they had forgotten about the SL series

Well, I am not looking for a new camera so I am not fully updated on the exact ingredients of those new cameras. But the Canon 4000D is by some considered a joke, a 7 y.o. Canon camera that has been given a new name they say. And it is said to be the cheapest entry level camera available. You can get one of them for every day of the week for the price of the Fuji X-H1.

New in the K1, not very much I think. It has mostly minor improvements but the ability for hand held pixel shift high res photos may be a big improvement if it works well.
No, I had the Sony A7III in mind. Seems to be a great camera on the way from Sony.
Yes, I had the Fuji X-H1 in mind.
Canon is all over the media with the new M50 and their latest brilliant camera the 4000D

Pentax K1, a new version was announced a few days ago. Also a new Sony was announced a few days ago and a new Fuji also and 2 new Canon cameras. I think that is quite a good selection of new cameras from last month and nothing to complain about there.