If your alternator died you would run out of the juice and the car would fail to start after some driving as the alternator would not be charging the battery.
Since the breaks run on vacuum and a vacuum leak would lead to rough idle I would check for a break or tear in the vacuum lines.
1992 325i / Briliant rot - SOLD @ 301,000km
1998 318is / Arktic silber - SOLD @ 207,000km
2007 335i / Jet Black - CURRENT @ 28,000 km