My main questions is: I am told the only PCU I can upgrade to is the I7-7700 and not much better than what I have. Is that true? 
My second question is: I am looking to upgrade the current 300W PSU so I can get a decent GPU.  The PSU is ATX so that's makes it easy but it's compact and finding 600W that can fit is a bit tougher.  It looks like the dimension's of the PSU are: 140mm 150mm 86mm anyone install a 600W or bigger PSU in the desktop before? 
Current Specs:
- 7th Generation Intel Core i5-7400 Processor (Up to 3.5GHz)
- 32GB DDR4 2400MHz
- Connectivity- 802.11ac wireless LAN, Gigabit LAN. Drive Interface-SATA 6 Gbps. 1TB M.2 SATA3 SDD
- Geforce GTX 1050
- Windows 10 Home
. 
[Edited the thread to add issue detail]