Bleamy

Short answer: Yes it will fit don't worry.
Expansion slots refer to those tiny metal lips you had to unscrew to put your current GPU in. Almost every case will fit a 3080Ti and below because they use the standard "dual slot" thickness. Some 3rd party cards will be thicker than the FE thickness because they might have bigger coolers requiring the use of a 3rd expansion slot.
Your case has 8 slots.

No, it won't hurt it. The B450 does support the 5000 series, but not without a BIOS update. This is likely where the confusion lies from the comments you've read. If you get no post from it, assuming you have everything hooked up correctly with a discrete GPU, then you can utilize the BIOS flashback feature of the board to update to a BIOS that does support the 5600x. 

if you cant really stretch the budget would go with this
PCPartPicker Part List Type Item Price CPU AMD Ryzen 3 3100 3.6 GHz Quad-Core Processor $99.99 Motherboard ASRock B450M PRO4 Micro ATX AM4 Motherboard $85.99 @ B&H Memory G.Skill Ripjaws V Series 16 GB (2 x 8 GB) DDR4-3200 CL16 Memory $57.99 @ Newegg Storage Western Digital SN750 500 GB M.2-2280 NVME Solid State Drive $62.99 @ Newegg Video Card Gigabyte GeForce GTX 1660 SUPER 6 GB GAMING Video Card $239.99 @ Newegg Case Cougar MX330-G ATX Mid Tower Case $51.98 @ B&H   Prices include shipping, taxes, rebates, and discounts     Total $598.93   Generated by PCPartPicker 2020-08-12 06:41 EDT-0400   *buying an extra fan for intake is recommended

Then I'ts pretty smart to keep it in my opinion