Depends on the age of your PSU and which one it is. Looking at Jonnyguru's guide, it doesn't look like the CX450 has some really old models
http://www.jonnyguru.com/forums/showthread.php?16610-Corsair-CX-and-CX-M-quot-cheat-sheet-quot the main question is what color is its label. If the label is green & black those are the poor quality CXs. If your CX PSU is 4ish years old I would look at replacing it as well. Reason being it has a 5 year warranty and realistically that is all you can expect from that budget PSU.
The motherboard in that case could be removed, theoretically. Last time I tried to remove a motherboard in a prebuilt computer it didn't go so well due to a proprietary screw. I would say just bite the bullet and change to a new case and then you won't have to worry.
RAM should always be bought in pairs. That is the only way that you can guarantee that 2 sticks will work together. You can always add another 2x8GB DIMMs later to get 32GB. Just know that there is no guarantee that it will work correctly. If you go that route you want to make sure to get the same speed, CAS, and brand of RAM to give you the best chance of it working.
Here is a new configuration with a cheaper CPU. This is still a very good CPU and the motherboard supports the Ryzen 3000 line and should also support the 4000 line with a BIOS update.
PCPartPicker Part List
CPU: AMD Ryzen 5 2600 3.4 GHz 6-Core Processor ($119.99 @ Newegg)
Motherboard: ASRock B450M/AC Micro ATX AM4 Motherboard ($84.99 @ Newegg)
Memory: GeIL EVO SPEAR Phantom Gaming 16 GB (2 x 8 GB) DDR4-3200 Memory ($67.99 @ Newegg)
Case: Fractal Design Focus G Mini MicroATX Mini Tower Case ($62.98 @ Newegg)
Power Supply: SeaSonic FOCUS 550 W 80+ Gold Certified Fully Modular ATX Power Supply ($94.99 @ B&H)
Case Fan: Fractal Design GP12-WT 52.3 CFM 120 mm Fan ($13.39 @ Newegg)
Total: $444.33
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2020-03-24 13:27 EDT-0400
I have included a good budget case. There are other options, especially if you don't need/want the DVD drive anymore from your current build. If you don't want the DVD drive I would look at the Fractal Design Define Mini C. It is a better case than the Focus G Mini and include sound dampening material to make it almost silent. The PSU listed here is another option. At 550W even with the higher TDP 3600X you can drive a GPU up to a RTX 2070 Super/ Radeon 5700XT. Anything more and you would be looking at a 650W PSU, but for just about any single GPU system a 650W is all you need.