1) Does it change, even slightly, due weakening of the last consonant sound? 2) If it does what is this phenomenon called?
The general process is known a lenition, which unfortunately refers to very many different processes. The underlying idea is that θ is "weaker" than t (likewise f,x compared to p,k), and one of the environments where this happens is postvocalically (with or without a tautosyllabicity condition). However, the term also encompasses the changes t → d,h,ʔ,ɾ. Usually, such a lenition takes place right after a vowel or glide and not a consonant, so if "r" is included in the context, one may reasonable suspect that "r" is a vocoid ɹ as in English, and not a trill. The physical mechanism beneath the process is not clear, but seems to have to do with delaying the transition from a very open vocal tract to a closed one. If the process were triggered only by preceding r and not a vowel, that would be a typologically novel process.