Welcome Kayla, I am gonna answer your three questions by order:
1) No you can't add a "س" before the "ب" nor can you add a "ب" before a "س" in a present-tense verb or a future-tense one. Still, if this "س" is an original part of the verb, then you can. I.g. "سبح" > "بسبح" to conjugate it from past to present.
2) In fact, for the Levantine Arabic I can't remember that I've heard someone using "سوف" or "س" to talk about the future, unless it comes in a sarcastic language! We rather use "رح" or ,shorter, "ح". And what matches the previous rule matches this one too, I mean you can't add these suffixes with "ب" unless it's a part of the original verb.
3) No you shouldn't add "ـة" with "عم", it works both for males, females and plural nouns. But, mainly, we use "ب" with the verb coming after "عم", so you should have said, "عم بجلس" or "عم باكل". It's ok to say "عم أجلس" or "عم آكل" but the former are more common.
P.s. I hope you do not confuse the dialect with MSA, because this is considered annoying, in my opinion, not because you will apparently be known as foreigner, no, but because you may find a small problem to fitting in with people! You may rather focus on MSA now, the dialect will be much more easier then, But not vice versa!!