shrimpgfx

Not always! Like now with the LGA 1151 Socket, there's about 4 generations. the 6th, 7th, 8th and, 9th. There's different motherboards that support some of these chips. Like a 200 series board is usually for the 7th gen CPU's but` if you tried to put a 8th or 9th gen CPU in there, it won't work. Basically speaking, the CPUs are not backwards compatible with older Mobos. Or something like that...

Places like eBay, gumtree/craigslist type of websites, local classifieds etc.

Here is the list of compatible CPUs. For some reason it doesn't show the i5 2400
 

It's supports up i7 3770. Which should be fine although it doesn't show the i5 2400

250W is plenty for that CPU and GPU. 
 
Although I'd personally take the 8600GT out, as it's basically the same speed as the HD2500 graphics in that i5-2400. If you
need a GPU for whatever reason, get something like a GT730 GDDR5 on the cheap.

I have not seen a PC that CPU whitelists for any reason other than CPU TDP being too high, or if the bios doesn't have the required microcode, so it should work.

Then yes the PSU will be fine.

its all to do with the brand and models. For example kingston and corsair value rams are a big no (too many error prone rams despite warranty). Go with proper ram such as team dark, g.skill, crucial, corsair, kingston but no value rams or generic rams (cruicial standard ram is fine though). Some standard ram that offer hynix/samsung chips are fine too as long as they are branded under a decent brand.
 
Many people dont know but patriot is one of the crappy brands for ram.