Should you ever repeat the subject "我“ in a sentence?
Unnecessary.
In spoken language it is acceptable and actually quite common. In written language it should be avoided.
Depends on the context. In your example it doesn't sound awkward at all.


Side note: As pointed out by this article, in Chinese, using the same word again and again is not as awkward as bad repetition in English and sometimes it's the only way to satisfy grammatical requirements. Not directly related but similarly, unnecessary repetitions in general have more appearances in spoken Chinese than in English and sound less awkward. You should not feel bad about it.