Even a completely green dwarf won't die to the training spears in the danger room if he's covered in armor and a few leather cloaks (have a newby carpenter make the spears to be sure). I will assume you are playing 3.18 (latest version).
Yes military training is slow if you don't use a danger room, but seeing no skill increase after 10 years is definitely not normal. I have had good results with the following schedule: 6 months training 10 minimum 6 months no scheduled order (civilian jobs all off all the time). The dwarfs will do individual combat drills in the time without schedule (raises their weapon skill, they need to have a weapon equipped of course). They will do demonstrations and spar in other months. For this to work the squad has to be equipped all the time (don't change their uniform to inactive:civilian clothes).
If you use dwarf therapist you can screen the migrants for dwarfs that already have some combat skills (shield user primarily as it trains the slowest but helps a great deal with a good quality shield), and possibly ones with some levels in student and teacher social skill. Put a few of these guys into each squad and you should see some better progress.
I think what might be happening to you is that the constant switching from civilian to soldier every month makes your dwarfs never finish any training activity (low skill soldiers take a long time to <organize [combat skill] demonstration>).
As for your flux problem if your parent civilization has a diplomat you can request the stones in the stone section while doing the trade agreement (request all flux type stones they have available), and additionally request steel and pig iron bars.
I don't want to spoil anything but know that there are rumors of a metal that is even better than steel.
Make max 3-dwarf squads for training. Train around the clock. It helps to have them at similar military skill levels initially (ie. all 0s).
If their barracks is right next to dining hall and booze storage, they will level up from 0 to 7-8 in their weapon and fighter skills, less so in others, in just one year. This way, if you dont play some Fun Challenge but a normal DF fort I dont think you ever really need to use a danger room.
Try this as well, you can also make flasks and backpacks to lower the time drinking and eating takes.