It depends on how fast the comet is going.
Comets
Why do comets have tails
Some comets have tails reaching 160 million kilometers long.
No, they do not burn only comets have tails.
yes
No, that would be comets.
Comets
rocks and dust
When they reach the inner solar system.
In the sense that an observer can see tails on comets - no, the gravity and composition of Mars is not favorable to the production of a tail.
Because they aren't traveling towards the sun. Comet tails are caused by debries being burned off.
yes