When expressing your opinion, you may use either of the two. «Счита́ть» implies that you think so because of your views, or because that would be your decision, or because you gave it some thought. «Ду́мать» can mean a lot of things, a random, incidental thought included.
Basically, you just have to know that «счита́ть» may mean something other than "to count", and as for using it yourself... well, depends on your exposure to Russian.
«име́ть» is a formal verb for "to have" used in business and official language (у кого-то есть что-то is neutral). However, there are a few set expressions where the verb can be used even in normal speech.