how long will it take to Process Resident Permit ?

Welcome to the forums.  Residencia starts at home.  I am told it can take 2 to 3 months to gather the required documents, get them translated, apostilized if needed and deposited at the nearest consulate. Once you get your passport and documents back you then come to DR and file then here along with application. 

From that point it can take 3 to 12 months.  Lately it seems the average is 6 to 8 months.

Cost of documents at home - no idea!   Lawyer including filing fees here range from. About US 1,000 to as high as US 3,000. 

There is a whole thread on residency you should go and read.  It's quite long so make yourself comfy!

We are going through this process now. The most aggravating thing, and there are a lot of aggravating things about this, is the Spanish translation. Our attorney indicates you must have the RD embassy translate your documents. If you have someone else translate them -  a third party service for instance - they may require the docs to be translated again once in RD. Having the consulate translate may be more convenient but their translation fees are twice as expensive. Just something else to be careful of.