I am native english, and you could say you have issues with someone or problems with someone! You have to remember though, issues may not always mean something very bad, but mainly means something that may need sorting or fixing. Like i would say i have got issues with my phones, and that implies that they can be resolved. To be honest, as a native speaker both phrases are used in England when regarding to both of your scenario's, so taje your pick to whatever you feel fits the situation better for you! :)

1) No, “I have problems with my cellphone” means "you" are facing difficulties in using your phone whereas " my cellphone have problems" clearing means its "the cellphone" that has problems. 2)Well first of all, both "Obviously, A have issues with B " and "Obviously, A have problems with B " are fine to say. but then when you say "A have issues/problems with B" - it will mean that it is A who is angry on B so its more one sided (blaming A) So...I think you should say "Obviously, A and B have issues/problems. Hope that helps~

Firstly, learn about the third person singular. I'm having problems with my cellphone. My cellphone has problems. Jack's having problems with Jill. Jack has issues with Jill...this is totally different. issues = personal problems