Pronouns – How to Omit Personal Pronouns in Formal and Informal Language

That's not the gerund.  That's its identical cousin, the participle.  If it were a gerund, then you would use the genitive form "my":

• The likelihood of my doing this is small

In this example, "doing this" is a gerund phrase.  "My" modifies the gerund phrase.  The modified gerund phrase is the object of the preposition "of".  
 

• The likelihood of me doing this is small

In this example, "doing this" is a participial phrase.  Participial phrases can modify nouns.  This participial phrase modifies "me".  The modified objective personal pronoun is the object of the preposition "of".  
 

Because there's no visible difference between the gerund and the so-called present participle, it almost looks like "me" and "my" are doing the same job.  They aren't.  The "me" acts as a modified object; the "my" acts as an object modifier.  Of course, in both cases you end up with some modified object for the preposition "for".  The overall meaning of each is much the same, and the choice between them is often no more than a question of stylistic convention.

If it helps, my personal preference is for the gerund construction.  I prefer the action, rather than the person, to be the literal object.

OK - my background is as a native British English speaker.

1) If I knew you were coming, I would've arrived from work earlier. This is perfectly easy to understand, though as you correctly say, the grammar is not correct. "Had known" is really needed. Still, some native speakers will say this.

2) If I knew you would/were gonna come, I would've arrived from work earlier. I find use of the contraction "gonna" the worst part of this construction. I think it may be more acceptable in American English. The same comment as above applies, of course, to the verb.

3) If I knew you had come, I would've arrived from work earlier. This sounds unnatural and needs a slight pause in thought to understand. I'd suggest you avoid it.

To a British English speaker all of these constructions sound a little jarring, but in informal situations, native speakers commonly use constructions which are grammatically incorrect. There is a danger in formal situations, that a native (British) English listener will assess your level of education or ability, to be less than it really is, if you use constructions like this. That will also depend on factors like the age and background of the listener.

Incidentally, and again in British English, the contraction "I'd have" is probably more usually used, than "I would've" unless there is emphasis on the "would".