They are all valid arguments, or can be made so quite simply. Being valid only means that they commit no formal fallacy. Begging the question is often referred to as a fallacy of presumption or a fallacy of assumption because the error is in assuming what one asserts to be proving. The example you give is not a model of logic, but a model of a valid argument in predicate logic. This model does beg the question.
Validity is independent of the truth of the premises and vice-versa.
Look at this one step at a time. A1 is the unsupported assertion that abortion is murder. S1 is the unsupported assertion that all men are mortal. The support for these assertions, if any support is to be found, lies outside the syllogism. Steps A2 and S2 don't seem to be very contentious.