Rebuilding, truncating etc SQL Server 2008 maintenance
Your questions cover a lot of scope for SQL Server database maintenance.  We need to address two areas here:  Backups and Index Maintenance.

Backups

The first thing you must understand before you can properly manage your backups is your recovery model.  This will determine how your transaction log is managed by the engine.  The simple description (the "real answer" is far more involved) is that your log file contains the records of each transaction that has occurred in your database.  In relation to that, your recovery model tells the engine whether or not you want point in time recovery (Full/Bulk Logged if you do, Simple if you don't).  Based on this information, the engine will remove records from the log file at checkpoints if it considers them safe to remove:


Full/Bulk Logged:  Since point in time recovery is desired, log records will not be removed until they have been safely backed up.  The engine needs to ensure that these log records can be made available for recovery.  Note, this is different than a full database backup.  If you need to restore your database, you will require both a full database backup and attendant log backups.  More detail on this restore process can be found here.
Simple Recovery: Log records are removed if transactions are completed.  Since point in time recovery is not desired, the engine will not retain the log records.


In regards to your other concerns, the backup operations are done online, so they won't directly impact your database.  Full backups capture a point in time, so any previous files will represent a previous point in time and, if you don't need those previous points in time, you won't need to retain those older backup files.

As for a backup schedule(frequency and retention of files), this is very much of an "it depends" answer.  It is discussed in more detail here.

Index Maintenance

This is a MUCH deeper topic, but essentially what you're looking to do is manage your index fragmentation so that it does not impact performance.  There's a lot written out there on what it is and how to manage it.  ToadWorld is a good place to start on how to manage your indexes and what index maintenance means.  This can impact use of your database (though the database will remain online for the operation), but there's lots of different factors around this impact and how to manage it.

Maintenance Plan

If you have DBA resources in your company, these tasks are within their bailiwick and they will likely have tools and a roadmap for managing these already.  If you don't have these resources, there are several tools that can be leveraged.  For maintenance as a whole, Ola Hallengren provides some free tools for this that are highly regarded and recommended in the SQL community.