JAR ops 1
If you search the interwebthing for the above it will give you some info.
I know its now EA ops but the EA publications are near on impossible to find free of charge.
You can start an approach if your minimums are out of limits. If you do not have the minimums by reaching the outer marker/1000' or equivalent position, you must go around.
If you did have the minimums when starting the approach but went below the mimimums after passing the criteria stated above, you can still carry on to your MDA/DA.
In essence you have two trap doors.
I am not sure what your job is and what your responsibilities are so cannot answer your question about choosing the different alternate.
We would obviously take the whole weather picture into account (i.e widespread fog everywhere) and make an informer decision.
Hopefully though the above helps.