I would say that your sentences are all correct, according to the construction, In an addition, some tips here may give you subtitle details on expression.
1, The first 2 sentences with 把, better put 了 right behind the verb给.
我把那支笔给了我的妹妹。我把一支笔给了我的妹妹。(the past tense)
我把那支笔给我的妹妹了。(To imply that you don't have that pen anymore. Because of the 了 in the end of the sentence.)
2.The last one is a drill of the present progressive, the 正 is omitted from 正在. Look :
-----你(正)在干什么?
-----我(正)在把这支笔给我的妹妹。
Absolutely, you did good job.