1 Does he have plenty of time? A) I haven't either/ B) neither have I/ neither do I . Which one is correct?
Personally, I would pick "neither do I". The reason being that have is the actual verb here and not an auxiliary one. Compare these two:
I have money, don't I?
I have spent all of my money, haven't I?
See the difference?
2 I'm lucky: Could you say: I have luck?
I find no special reason to object it, though I don't think I've ever heard it...
3 Luckily enough I.... Could you say : Lucky enough I...?
You could say: "I was lucky enough to...", but you can't say what you asked because luckily is acting as an advervb to the verb that comes behind I and lucky is not an adverb.
4 A) There seems to be problems B) There seem to be problems??
I think B
5 How many horsepower does your car have/ How much horsepower...
much. I can't say one horsepower, two horsepowers, etc. I could say one horse's power, two horses' power... but that doesn't make much sense