Just to expand on previous answer that was posted.
Just like George said, shrinking in general is not something that should be part of maintenance job. Rather log size miscalculations, some unexpected scenarios (such as uncommitted transaction, large and intensive DMLs etc etc) or insufficient amount of log backups can cause excessive log growths.
If your log size does not seem large enough, you should monitor it during busy hours, or during night time ETLs(If you have some) to see the average log size and change it if needed. Also make sure to set log size auto growth in specific MB size, which will mostly depend on your initial log size. More info could be found here Database log VLFs
Now to answer your questions:
1) No in general. But in scenarios i mentioned above, it could be helpful. Which is the only time when it should be used - out of ordinary situations.
2) If you determined you want to shrink your log file, you should be aware that the log file is made out of VLFs(Virtual log files), which are gradually filled one at the time. Once all of them are filled,if you reached your log maximum size, log auto growth will happen and depending on size will grow in 4/8/16 VLFs. Once the log is backed up, these VLFs will become empty again (you will always have some in use, so it can track current LSN). To keep it short, once you backup you log, you can check used and unused VLFs using
DBCC LOGINFO command
Fields to note here that are useful for shrinking are File Size which is the size in bytes, and Status which can be either 0(unused) or 2(used).
The amount of % or MBs that could be shrunken is sum of unused VLFs - 1VLF.
Be aware that shrinking only happens in VLF amounts, you cannot shrink it in desired MBs such as 5,10,12 etc, unless it fits the summed size of used VLFs. Always make sure to check messages after shrinking occurs.
3) Shrinking does not remove indexes, since shrinking removes only unused(empty) VLFs. If you might have thought, if shrinking database files defragment indexes - yes it does but its off the topic.