I noticed some sketchs where analog pins are defined with an A preceding the pin number.
Is that mandatory?
No. And, technically, it's not even correct. The An aliases are defined for when the analog pins are to be used as digital pins. When they are used as analog pins, just the number should be used.
But, for some bizarre reason, the aliases are also mapped correctly to the proper pin number when used with analog functions. That doesn't speed up the process.
If I want to use let's say the analog 0 and the digital 0 at the same time, would that cause any conflict?
Only with Serial. No, the pins are on opposite sides of the board. The digital pins are completely separate from the analog (nature of) the pins (with dual nature).