Yes . many do but you need to call to coordinate that . too difficult to do online
The economy resorts have adjoining rooms available but total of 4 double beds wouldn't cover your group, you'd need 3 rooms at e.g. Pop Century. I don't recall there being an extra extra door to get 3 in a row adjoining - i've only seen that rarely elsewhere. The "Lockoff 2 Bedroom" is a 1BR Villa with adjoining door to a Studio villa. This can increase your options compared to a standard 2BR. Extra lavatory and extra kitcehnette.
Yes a lot of the resorts do. But i would call. They also can make sure you have cribs for the infants.
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