Can I only give reputation "once" per thread when I close it?
You can rep whenever you want to, solved and unsolved threads. You can rep a post in a thread where you have never posted a single post. You can rep several posts in a same thread, the only restriction being that you have to rep 10 other members before you can rep the same member again.
Am I only allowed to give reputation while the thread is open (prior to marking it solved) or does that power continue after I actually press solved?
See above. You cannot rep very old posts but other than that, you can rep whenever you want to, any member you want to, as often as you want to (same member only after repping 10 other members), in all threads solved or not, in threads started by any member.
Notice that you cannot rep in
News and
Chillout subforums.
No order of operations i.e. step 1 close thread... step 2 give reputations (not so demanding like that but I'd like to know what closing a thread stops me from doing before I do that!)
Marking the thread solved does not close the thread nor has it any whatsoever connection to rep giving, you can still post in that thread as can other members and you (or anyone else) can still rep posts in that thread. The solved status is only there to help members and guests alike browsing the forums to see that this thread contains a solution. Too often OPs forget to mark thread solved so the Solved indicator missing does not automatically mean that the issue is still unsolved.
There was a mention about "reputation power" link or button in myu profile, indicating how much I have to give... I must have nothing... as i can't find the said button....
Reputation power is based on your status, how long have you been a member, how much rep you have, how many posts you have posted and so on. The longer you stay, the more you post, the more rep you gain, the more rep power you will have. It determines the amount of rep points you give to another member when you rep him / her.
Rep power is capped at 45 points, when your rep power is more than that you will give 45 rep points. For instance if I would now rep you you, you would only get 45 rep points although my rep power at the moment is 1,250. It would be insane without a rep cap, a few reps from senior members could give a member with two or three posts a medal.
Go to your UserCP to see the last reps you have given and received, you'll find your rep power there:
(on another note, there was a mention in one of the FAQ of a print menu button upper right... I clicked on lots of things... not there.. can someone show me which icon it looks like? Would be nice to print a printer friendly copy of some pages if I can when people give good advice in my and other threads!)
Each page in every thread has a
Thread tools menu,
Printable version option can be found there:

XP VM USER (guess I got stuck with name from my first posting..... and I will not violate rules by making another name for myself as that was a rule in the Forum rules not to do it)
John (our admin z3r010) has been flexible regarding this matter and allowed one username change. Contact him requesting a username change.
Notice that I cannot promise your request will be granted, John alone decides

.
Kari