When asking someone else to do a favour, one would append ください or くれる. For example, 手伝ってください or 手伝ってくれる to either mean "please help me" in the former case and "can you help me" in the latter case. What if I were to say 手伝ってくれていい, would this mean exactly the same as 手伝ってくれる? Or does no one actually say it like this? Also, is the difference between 手伝ってください and 手伝ってくれる, only being that the former is taking a stronger stance in asking someone (for a favor) to help, whilst the latter a lighter stance, such that it isn't really forcing but merely asking in a light tone?
手伝ってください is a kinda straightforward "Help me please". てください is a polite imperative so like with every imperativ you don't really give the other person a choice (In a grammatical sense). Same with 手伝ってくれ(よ) which is the plain imperativ which sound like a "Cmon, please help me" or 手伝いなさい as "Help me (now)!" (Of course depending on the context)
Politer ways to ask for something would be 手伝ってくれる(?) and 手伝ってもらっていい？ Both give the other person a choice and therefore sound nice. They are on the same politeness level, but people have personal tendencies. Some examples:
As mentioned by other people the いい wouldn't work out with the てくれる so you would have to combine it with もらう.
You probably mean spoken language or "cartoon Japanese", as using くれる to end a question would (if writing) need a question mark afterwards. (And this is of course an indication that is is not formal and belongs more to something like cartoons).
One advice to you: Just don't use the structure "手伝ってくれる？", unless you know what you are doing.
手伝ってくれる？ is not about "taking a lighter stance", if having to choose, it could be thought of as the opposite, and also be rude depending on the situation.
One might use it in situations where one in a way "has the right to assume" that the person will do as you request. For example, at work, the boss might use "手伝ってくれる？" when asking his/her subordinate to help. On the countrary, if you would use that to ask your boss to help, you might soon need to find yourself a new boss (=get fired)
The "手伝ってくれていい" is something you would not say, as the "いい？" would require "the opposite direction" ie あげていい？ would work. (Sorry for lousy explanation, but while I am bad at using the search function, I am quite sure it has been answered somewhere on this forum already.)