Sounds like you have multiple issues.
The first thing you must do, though, is repair the charging system. You likely need the alternator replaced...however, have the charging system checked first to verify this.
Once the charging system is functioning, you can verify that codes are valid. Sometimes codes can occur due to low battery voltage. Although the lean fuel trim code (P0171) and the transmission range sensor code (P0708) are probably valid, you need to fix the charging system first to be sure.
If the codes reoccur and the signal lights are still out:
P0171 could be a mass air flow sensor issue, a vacuum leak, a fuel pressure issue, or an oxygen sensor issue.
P0708 could be a faulty transmission range sensor, could be a faulty wiring connector, or both.
The signal light issue could be a fuse, relay, signal switch.
Whew! Good luck...just take it step by step.