Gremlin_FLG

To save from static damaging stuff, buy a static wrist strap.
 
Unbox the PSU and connect power cable to the wall outlet. 
Don't connect the PSU cables to anything. Connect the Wrist Strap clip to the grill of the PSU Fan. 
Turn the switch on .. 
 
And you are all set.. 
 
 

New one in next years is vague
 
All depends on how much you want to spend and what equipment you currently have,, 
 
Are you prepared to buy new memory, new motherboard?

I see what you're trying to do, but keep in mind that your existing 550w PSU is "550w max load" and it's never a good idea to run a power supply over about ~80-90% max load for longer than brief periods of time(seconds to minutes). Running a PSU at close to 100% for a long duration can cause damage to the unit and be potentially dangerous.
 
However, You can wire a switch into the PSU to turn the unit on and off independently of either of the PC systems you're powering. This would allow you to keep the unit on when "the main PC" is powered off. You would have to alter the main 24 pin cable to do this though. You can see an example of this in the exact alternate use case you're describing: https://www.newegg.com/battleborn-131106131282/p/35Y-000B-00009?Item=9SIA85V3DG9612&nm_mc=KNC-GoogleMKP-PC&cm_mmc=KNC-GoogleMKP-PC-_-pla-_-Data Adapters-_-9SIA85V3DG9612&gclid=Cj0KEQjwzZe8BRDguN3cmOr4_dgBEiQAijjVFgmCuhgUIFaTzN08YDT6ixnAPlpPIMjx4K_bMV4NVc4aAiTN8P8HAQ&gclsrc=aw.ds
 
Do keep in mind though that it's much safer to just buy a dedicated PSU for your mini second system.

From the video, looks like system is on, no display of system logo ? Can you go into bios at all?

buy a psu splitter, phanteks made one http://www.phanteks.com/PH-PWSPR.html
 
But really, best option is to get a second psu, those splitters aren't cheap.

Assemble as much as you can outside the case first.
Do a test boot outside the case too
cable manage as you go

mount that rad fans before your install the radiator
plug in whatever psu cables you need to the power supply before you install it