Can you use items, power cores, lasers, ext that another character has given you? even if you cant buy it?

yes you can use the items players give you
but some items still require a licence lvl
or you can go to any corvus (pirate) station in Grey Space with your items and equip them with no requirements
you can also buy ships etc. from corvus a few lvls below normal
requirements e.g. a Behemoth in nation space is 8 trade / 4 mining but in corvus its 5 trade / 2 mining
hope this helps

Yes. Items requiring a license to buy can be used. If it requires a license to USE, you can't play with the new toy.

Simply put, licenses prevent equipping, not buying of said items. But some people, such as Corvus, ie the Pirate faction, will equip it regardless of your license level if they like you. Get high faction rating with Corvus if you can. Helps immensely as a newb.

Also, because no-one else said it yet: Greyspace has a tendency to become a "black hole" of sorts for newer players. Do not home in grey space unless you can handle the possible event where you get killed over and over trying to leave. Some pirates will let you by because your licenses are low, but some won't, just to prove the point that greyspace is dangerous.

Items purchased at Corvus stations are much more expensive than they are anywhere else, so keep that in mind. You could go bankrupt pretty quickly if you don't have much in the way of money, and you keep encountering the second type of pirate I mentioned above.