pomgod

If you're still not planning on getting the GPU now. Just wait for ampere and big Navi which should be released/ announced later the year. 

bottleneck? technically there is always a bottleneck, some workloads are cpu bottle necked and other's are gpu,  in a sense that the 3500 will slow down the 5700, then no the 3500 will be fine for the most part. 
what about the 3300x/3600? what are they priced at? also consider the 5600xt, like a pulse model which comes with flashed with the new firmware, they're basically a 5700 with a smaller frame buffer. 

Bottleneck? Unless you plan on going 240FPS in Fortnite all Low settings or exclusively play Battlefield 5, no, the 3500 will keep up just fine. 
 
Have you considered going with a 3600 and 5600XT instead though? The 14Gbps vBIOS models, like the Sapphire Pulse or Powercolor Red Dragon, are super close in terms of performance to the 5700, but with the 3600 you're getting double the threads.

Should be fine

It'll depend what the controller the case comes supplied connects to... esp. for power.
It may work perfectly fine off the remote, but that may well be something you only find out by buying the case.

standard ATX so any ATX, micro ATX, and mini ITX motherboard will fit