もらう and もらって when used with various forms of verbs

Question

What happens when I post-fix a って to もらう. Example:
手伝ってもらって.

I know 手伝ってもらう means I receive the favor of someone helping me. But what does conjugating もらう to its て form does?

Also, in its causative form,
手伝わせてもらう - A made B help me (as a favor for me)

If I am to conjugate this to 手伝ってもらって, what does it mean?

And finally, its passive form:
手伝われてもらう - Same meaning as 手伝ってもらう possibly?

Again, conjugating this to 手伝われてもらって, what does this mean?

Answer 1

もらう means the subject receives a favor/thing from someone else. The subject is typically "I", but it doesn't have to be so. As always, the implied subject depends on the context.

私は手伝ってもらった。
I got help (from someone).

彼は手伝ってもらった。
He got help (from someone).

手伝ってもらった。
{Someone} got help (from someone).
_{(This "someone" is typically "I", but it can be anyone depending on the context.)}

The te-form can form a request, as you probably know. Therefore:

手伝ってもらって。
(You should) Get help (from someone).
Let {him/her/someone} help you.

させて + もらう is not so uncommon. Here, the "favor" itself is a causative expression. Note that させる can also describe allowance:

私は手伝ってもらった。
I received a favor of helping (me).
I got help (from someone).

私は手伝わせてもらった。
I received a favor of letting me help (someone).
Thankfully, I was allowed to help (someone).

られて + もらう is a very rare combination and you may want to forget it for now. In case you're curious, it's possible to say something like this:

私は彼に怒られてもらった。
I received his favor of being scolded (by someone else).
I got him to be scolded (e.g., on behalf of me).
_{(It's far more natural to say 彼は(私の代わりに)怒られてくれた.)}

Answer 2

手伝わせてもらう would simply mean "help (someone)". The nuance is that you are helping another, whether they wanted the help or not.

手伝ってもらって would be "to have someone help", as in:

「あの人に手伝ってもらってね」

"Be sure to have him help you." or "Be sure to ask him to help you."

or in the middle of a sentence it would indicate "having someone help, (...)". E.g.

「彼に手伝ってもらって、早めに終わらせるんだ」

"Have him help you so you can finish early."

I've never heard anyone use 手伝われてもらう (and by extension, 手伝われてもらって). As an example,

「A君には手伝われてもらうぞ」

while confusing, would technically convey the impression that A-kun does not want others to help him with some specific task, yet the speaker wants A-kun to accept other people's (not the speaker's, but in general) help, in terms of that specific task. Practically no one uses this form, though, unless their intention is to play with verb conjugation.