Is a comma needed?

Dear native English speakers,
I have a question about the usage of comma.
Which would be accepted in each case?

(1a) Mary ran toward me smiling.
(1b) Mary ran toward me, smiling.

(2a) The little children walked down the street singing merrily.
(2b) The little children walked down the street, singing merrily.

(3a) Fred was drawing a picture listening to the radio.
(3b) Fred was drawing a picture, listening to the radio.

(4a) Jane went through the drawers looking for the key.
(4b) Jane went through the drawers, looking for the key.

(5a) The big earthquake hit our city causing great damage.
(5b) The big earthquake hit our city, causing great damage.

Thanks in advance.

Hirashin

Honestly, I have no clue. My instinct is that the comma is required in all cases except for #4, but it's quite commonplace for native speakers to omit necessary commas, so I don't know where the line between necessary and unnecessary really is.

Thanks, Julimaruchan.
I asked about this here because one of my students asked me about this punctuation and I couldn't answer it.

I think they are all ok and follow this rule:
to set off a nonessential or nonrestrictive clause, that is, a clause that embellishes a sentence but if removed would leave the grammatical structure and meaning of the sentence intact.

One bit of advice I can offer in these situations: usually, it's easier to read a sentence that's missing a necessary comma than it is to read one that has a comma that shouldn't be there. I've seen many people who need to go back to English class (I say that because many of them are native speakers) write things like this; note that all of these are syntactically incorrect:

* Eating vegetables, is good for your health.
* I do not think, that you should do that.
* Some people say, that my English is bad.

As an English reader, my brain is trained to treat any comma as a pause, and treat any pause as bringing me into another major section of the sentence. Essentially, after a comma, I expect to see an expression of some sort that stands apart from what preceded said comma. I can't get more specific than that because I don't know exactly how it works, but basically, excess commas like these make me drop small details from my short-term memory and force me to re-read the part before the comma again. On the other hand, having too few commas only makes me read the whole sentence at once; this can be a problem if it's a particularly long or complex sentence, as this one is, but I would still contend that dealing with a run-on sentence is less mentally taxing than dealing with a sentence that's been split into too many pieces, or a sentence which has been split at the wrong position.