Fast Recovery in SQL Enterprise Edition Starting with SQL Server 2005 and all later versions, Enterprise Edition includes a feature called "Fast Recovery".

a) Does fast recovery use multiple OS threads to perform "REDO" operation?

b) Does SQL Server write to the transaction log in parallel spawning multiple threads or is the log written sequentially so only one thread is used for writing to the transaction log?
Understanding Logging and Recovery in SQL Server
  
  Replaying log records is called the REDO (or roll forward) phase of
  recovery. Reverting log records is called the UNDO (or roll back)
  phase of recovery. In other words, recovery will make sure that a
  transaction and all its constituent log records are either redone or
  undone.


Fast recovery allows a database to come online as soon as the REDO phase completes, before UNDO is run. This is made possible by lock logging, which records the locks that were applied by a transaction in the associated log record. 

Fast recovery reads the log records that will be UNDONE, acquires the locks, then brings the database online. The UNDO processing can then proceed in due course while other database activity occurs as the resources that will be affected are protected by locks. See Paul Randal's Lock logging and fast recovery post for the gory details.

REDO operations are single threaded on Standard Edition and Enterprise Edition with less than 5 cores. On Enterprise with 5+ cores, there is a redo thread for every 4 cores (reference). This is separate and unrelated to the Fast Recovery feature as far as I can tell.

In answer to your other question, a single thread is responsible for transaction log writes.