I'm not a doctor but I often enter to operation rooms and advicese on how to use our products.

We will have a congress ofmeeting about our speciality from tomorrow, but I' will not be attending it.

"Congress" feels like a bit of an unnatural term to use here. I'm not entirely sure what you mean by "congress of our speciality".
"Meeting" is likely the term you were looking for.

"I'll not attend it" sounds a bit like a British person refusing to attend, rather than a simple statement of fact. Here it is very common to use the future continuous tense ("I will be VERB-ing"). When these sentences are negative contracting "I will" to "I'll" feels quite British - it's not wrong, but a less common construction.

However, it willon't be noa problem.

"will be no problem" isn't wrong, but this construction is more common and natural here.

I have asomething more important thing.

As above, the original sentence isn't wrong, but this feels most natural to me.

Actually, wWe are expecting a second baby right nowcurrently, and the due date is coming soon.

"right now" might give the impression that you're in the room waiting for the baby. It's not wrong, though.

I hope that my wife and new baby will be safe forthroughout the process of delivery.

My daughter really wants to care for the new baby.