Health care labors often don't happen quickly, and that's an obvious problem. I'd suggest that you turn off all other labors on your chief medical dwarf if you haven't already.
Soap making is fairly straightforward, as long as you don't try to do it with lye you made yourself. Buy a couple barrels of lye from a caravan and it becomes simple. Get a kitchen, slaughter an animal, render some tallow, make a soap maker's shop, and make soap with the tallow and the bought lye. It's only really troublesome if you're trying to use self-made lye, as that naturally gets stored in buckets and you need it in barrels.
Plaster isn't working; don't even bother. Just make and use splints.
To remove bolts from dwarves, it's far, far easier to use the z-stocks menu than to search out individual dwarves. Once the goblins are gone, go into the z-stocks, scroll down to Ammunition, scroll to any ammot types with an F next to them, and hit (f) and (d) to unforbid and set for dumping all ammo of that type, or hit TAB, scroll down to the bottom, and just unforbid-dump all the 1-ammo forbidden stacks (forbidden ones are always at the very bottom). You'll need a working bookkeeper to use this method, but once you learn to use the z-stocks menu, you'll never, ever look back.
Part of the problem is also likely that you're not keeping your dwarves safe very well. You shouldn't have too many reasons for your dwarves to go outside, so why are dozens of dwarves getting hit every time an ambush/siege comes along? Make use of burrows to prevent dwarves from going into danger zones, look into defensive strategies to mitigate the ability of marksgoblins to shoot your people, deploy traps, equip and train your soldiers better, and just in general make your fort safer so you don't need so much healthcare.
Healthcare is still fairly new, and hasn't been polished very well. Still, it is usable and not terribly frustrating if you know what you're doing, and not just with the healthcare system itself. You may need to learn about extra tips and tricks that seem completely unrelated to the problems you're having.