Is it obligatory to pay the Zakat for the past two years on behalf of the deceased from the inheritance, taking into consideration the heirs' refusal to do so, and is it better for the questioner to pay the full Zakat from their share, or to pay a percentage of it?

Zakat (definition) is obligatory upon the deceased for the two years in which it was not paid, because it is not waived by death. It must be paid from his estate before its division among the heirs. The refusal of the heirs to pay Zakat is an error, and they are obligated to pay it for all the money. If they do not comply, then you are only obligated to pay Zakat for your share. Paying Zakat from house rent over a period of ten years is not permissible, as it delays Zakat from its rightful recipients without a valid excuse. Zakat is due immediately, and its delay is not permissible.