1- As a precaution, if a Kafir says Salam Alaikom to you, respond by saying “Salam” only or “Alaik” only, but not Salam Alaikom or Alaikom alSalam
2- They are considered Muslims legally as long as they do not show enmity to the Ahlulbayt (a).
3- Yes
4- Scholars don’t have a clear ruling on whether they are Muslims or not. It they claim to be Muslims and you don’t see anything from them that violates the necessities of Islam, you may consider them Muslims.
5- Those who clearly state Prophet Mohammad (s) is not the last prophet are not Muslims according to a number of scholars.