1. Why is there 了 twice here if I only called Little Li once?
我给小李打了电话了.
Ok, The first 了here means: have done someting, while the second one means the samething.but,most time, you can change the scond 了 to 啦。so,我给小李打了电话了.actually means :我给小李打了电话啦.
2. Would it also be correct to say 我给小李打电话了 or 我给小李打了电话 or 我给了小李打电话
the first two sentences are both right. and means exactly the same thing. 我给了小李打电话--if you say it to native chinese people, they can understand you, but it sounds a little bit strange, kinda of England-Chiniese.