Yeah, your characters can die and be revived after battle, but after a few rounds will turn to a crystal or item, and then they'll be lost forever (certain story characters like Delita cannot turn to crystal).

FFT is a lot about strategy. You have a better chance of a successful attack if you're attacking from the side or back; you can also utilize high ground for additional range for attacks. If a group of monsters is a problem, try letting them come to you and focusing on one at a time instead of running straight in and getting beat up.

After you're done getting the necessary Squire abilities, it's good to have a balanced party of physical and magic, and early on you'll want at least two characters capable of healing (you can have a fighter character that can heal if you just learn Potion from the Chemist job and then equip the Item ability as his secondary ability).

Fighting random battles is a good way to familiarize yourself with all of this. The random battle monsters do level up with you, but the story battles don't, so you'll still have some advantage going forward by grinding a little early on. A good way to do this is to kill off all monsters except one, which you get down to critical health (when it runs and hides in the corner of the map). Then you can just attack your own party or use self-targeting abilities like Accumulate (Squire ability) to gain JP and Exp.