Should I get the dtap vaccine for my adopted child?

Yes. If you have a vaccine record from a dependable source and that record verifies an up to date schedule, you can skip it.However, those from foreign countries often contain falsified entries just to meet exit requirements. I re-start the series appropriate for that child at that age as if they received no immunizations at all. There is no risks to doubling up on vaccines unless the kid is allergic.
Probably. As immunization records, particularly from overseas, may not be accurate, your pediatrician may chose to check antibody levels first if there is a possibility the vaccines were indeed given. If the records don't fit the schedule or if the care is in question, then the series should and will be restarted.