Heal song is great for healing your pet if you have a red or purple one you want to keep alive.
Once the pet is out of combat and starts getting health ticks, it'll be full in like 10 seconds.
Minstrels do kind of suck in group PvE, but you can try to make yourself useful (besides POM) by using a strong pet and stunning/peeling for your healers/casters. It is very easy to hold a high level pet on this server, even a purple one with 80%+ resist is controllable. You can get some really cool pets once you hit lvl 40+.
Finding a red/purple pet that hits hard or has a good dot, nuke, DD proc etc and using it to kill yellows solo can yield pretty good XP. I generally just maximize my task-xp if i cant find a group.
I recommend using high con pets in PvE all the time just to get used to twisting your songs and targeting/re-charming your pet. Remember you can put pet attack/passive/pet target etc to your quickbar so you dont have to click the pet window.
Dont put any points at all in stealth while leveling. If you want stealth in BGs, just use the free respec at your trainer and then spec back to "normal" for PvE