In Battlefield 3, (non-hardcore) I know that grenades can damage both enemies and teammates. Does this also apply to mortar fire? Am I hurting my own team with splash damage?
No, you aren't. Not physically, at least. If one of your mortar rounds lands close to a teammate (in non-hardcore), your teammate won't take any damage. It DOES cause their screen to shake horribly, which can be harmful if they're currently in a gunfight, as it throws off their accuracy and leaves them vulnerable to enemy fire without the ability to return fire easily. It only lasts for a couple of seconds though.
One thing worth noting, however, is this: If your mortars strike a friendly target as he is laying C4 or AT Mines, the mortar will cause these to detonate, possibly resulting in a suicide for your teammate.