This probably doesn't belong in this category but I didn't find a place for it, and let's face it, the mods need some work anyways.
I have been learning about punctuation and capitalization for dialogue, but it's quite complex and I have a couple of cases where I can't figure out exactly what to do.

The rules seem to dictate that one uses a comma only when the following is a dialogue tag:
"I suck," she said, and mimed the act.
But when the following is an action tag, it should be a period and start a new sentence essentially, ie:
"I suck." She mimed the act.

My confusion arises when the character's dialogue has ended, but my narration of the moment has not. So my instinct is to use a comma, because my sentence is not over, even if the character's is.

In this case, the character's sentence finished at "We lost track of time." but I opened the sentence originally with a dialogue tag ("she asked") and continued in a single sentence with a comma.
Do I have to full stop the sentence and create a disjointed second sentence? It feels awkward especially because it begins with "and", and I'd probably have to put a new "she" in there.

And what if I don't feel like using a dialogue tag at all?

Here it's even more confusing, because the second part of the sentence is describing the character talking about something, just not describing exactly what he said. So it's still dialogue, so I feel like the comma is justified, but going by the rules it seems I should also use a period and cut the sentence in two (and probably get rid of the "and").

I don't want to force myself to use dialogue tags everywhere just to be able to use commas, sometimes I want to write the dialogue and the narration close tight like this.

Is this a case where the em dash could be used? "Blablabla" -- and he also apologised.
From what I've read, the em dash is really reserved for interrupting a character's sentence, which is not the case here.
What do you think?

 

Your I suck example is just about right, though it is still an awkward way of phrasing it.

In the second example, you use a period when they stop talking, because that is the end of that specific action; a further action gets a new sentence. Then replace 'and' with 'She' - starting a sentence with 'and' is weak construction.

In the next example, again, period in the quotation, then new sentence. Your revision is correct.

The general rule is each action gets its own sentence, and each related set of actions - by a single character or group - gets its own paragragh.

Dashes are generally understood to imply that someone was talking or acting and was interrupted.

 

I guess my problem is I don't really understand why starting a sentence, or continuing a sentence with "and" is weak.
I like the flow of narration with "and" joining actions together. It feels more story-like for me and I'm not sure why.
Breaking up each action to their own sentence whenever it involves dialogue does seem to be the rule, I agree, from what I've been reading online. I'm not very happy with it though.

 

No shame in not liking something - but when that something is standard, understood methods of communication, folks are going to take issue with it.

I'd agree that having a few extra 'and's in your paragraphs and sentences feels natural; but that's because it is how we speak, and one of the tough things to learn about writing is that people speak and write differently. When speaking, we ramble on, we take weird pauses, we fill silence with 'um's and 'ah's and we interrupt and speak over each other all the time.

Writing cannot be like that. It's confusing, it's messy, and it's just plain ugly on the page. What you see on the page has to be digestible and understandable for your readers, even if you have to 'cheat' the realism a bit. This is one of the dirty little secrets of writing, and all writers do it - they have to, or no reader would know what the hell they were looking at.

Not to mention that, at this point, the convention is so ingrained, most readers don't even notice it anymore. Instead, they notice when writers don't follow it. It may sound more realistic when spoken out loud, but most readers would look at it on the page like something was wrong.

As for why you don't start a sentence with 'And', while it's largely a convention, it's considered poor grammar and is generally an indication that you could have structured the sentences differently and more effectively - as you did.

All that being said... there are exceptions. However, as with learning and developing any skill, until you have mastered working within the rules, you shouldn't be breaking the rules. Readers can almost always tell the difference between a good, experienced writer playing with convention and a newbie who is trying to sound cool or more natural.

It can be a very fine difference, coming down to word selection or rhythm or cadence of the sentence or paragraph. Usually, though, examples will jump out; if you ever read a passage and get a little tickle in the back of your brain, or need to re-read it to make sure you understood it, or just find yourself furrowing your brow and thinking, "That was awkward," then there you go.