So after playing a little fallout 4 I did a couple institute missions and looked around the institutes head of operations and wondered how did they get enough resources for everything? How did they have enough energy, resources and survivors of the war to be able to create such advanced technology?

http://fallout.wikia.com/wiki/The_Institute

Are you asking "how" as in addition to the available information/lore? Todd's answer would be "it just works"

even when it doesn't

I asked a similar question when i came upon the institute...only mine was "wait...you expect me to believe that ALLLLLLL of this is underground and remained intact post-war?....mmmm yeah ok"

Sadly because of this my playthrough of the game varies only so much.

That's exactly what I was wondering! How'd they even have enough food and equipment to even tunnel down that far underground, and how they managed to barely suffer any radiation damage after the bombs fell is baffling.

Here's the answer, Bethesda. If something doesn't make sense in their Fallout games, it's Bethesda. Remember how in Fallout 3 that the Brotherhood made base in the Pentagon, well where did they get the food and water and other resources? They were fighting the Super mutant threat in Washington and they were magically surviving on air?
Here's a post on Steam that illustrates the lack of common sense Bethesda has with their Fallout games.
https://steamcommunity.com/app/377160/discussions/0/458606877310719380/

And here's Pete Hines admitting they don't care about lore or consistency.
https://twitter.com/DCDeacon/status/668802348140109824