The IMEI number on the 6s is on the sim tray not on the back housing like the 6. You can buy blank housings with the components installed for about $20 on Aliexpress. I don’t think you will find anyone selling new OEM Apple housings as customs are starting to confiscate parts with an apple logo printed on them. The best thing to do would be to purchase an iCloud locked 6s that has a good housing and swap the logic boards.
If you are talking about the battery connector it is a common problem on the iPhone 8 I usually end up replacing it but for other people who suffer this after a battery replacement you might be able to manipulate the connector on the logic board with a pair of tweezers so as it fits in nice and firm.
This is a common problem with the 7 dock flex. I have just finished replacing one and had the same problem. I ended up connecting the dock flex first than putting the board in and working backwards. Hopefully there is not too much adhesive on yours so you can do the same.
This is becoming a common issue with the JC home button. We are recommending the HX brand. I have been told if you long press the home button the keyboard will appear but I haven’t got a device to try it on.
Arbaman is right about the small scale but it sounds like a good project if you have the right equipment. You should be able to remove and install these components with a hair dryer, quick chip smd removal kit, soldering iron, Kapton tape and some solder. Just melt the low melt alloy into the solder joints with a soldering iron than use a hair dryer to remove the component. Just be careful if that button is rubber, Kapton tape will not protect it. Try and tape a small heatsink on top. Just use an iron to resolder it on the board
You would need to test the screen on another phone or another screen on your phone to rule it out. If it is not the screen it will be the touch connector or the touch IC. You can set the phone up with 3Utools it has an option now that doesn’t require screen input.
The first thing to do would be rule out parts. If you don’t have access to another good screen you could at least disconnect the home button, front and rear camera connectors and see if it brings back full touch.