Do and don't in Dominican Republic

Do learn the language. If you aren't fluent, that's okay, but keep working on it. Don't wait till you can speak it perfectly to use it.
Do share: it's rude to eat in front of someone without offering them some.
Do be patient: most everything seems to take longer here. Getting angry will not get you faster service, it will just get you a bad name.
Don't constantly talk about how it's done in your country of origin.
Do learn to appreciate and cook the local food.
Don't be openly scornful of home remedies, even if you think they are silly. You don't have to use them, but be respectful and appreciative of those who offer their advice.
Do remember that loyalty to friends and family is a pillar of Dominican culture.
Don't expect most activities to start at the hour indicated. Generally they will start a half hour to an hour later, or even more, depending on the type of activity.
Don't eat on the street until you've been here a good while and  have learned what is safe (and gotten more accustomed to the local bacteria.)
Do observe how the nationals dress, and learn what is appropriate for your particular area. Sleeveless shirts are not allowed in most govt. buildings, and shorts mark you as a tourist in most areas.
Do learn how to drive. There really is a system. It might be best to observe a while before jumping right in.
Do find out about a little about labor law before hiring people. You might be in shock when you find out about maternity benefits, liquidation, and that in December that you have to pay a double wage.
Don't spend all your time with expats from your country. Make Dominican friends as well.

alabemos
Great post. Welcome to the forums.  I would add:

Do enjoy what the country has to offer and don't dwell on what it needs.
Do understand that there are many things you cannot change here, but at the same time there is lots you can do to help the community. Especially working with the children.
Do understand that the local Dominican is generally happy and does not want to change...why should he?

Bob K