1. you can find other freeware disk burners (among a ton of other good freeware), here
2. I know of that issue. The only solution is getting another (different) DVD burner, it's a rare enough issue that should not happen again to you. You can get one for near-free by scavenging older PCs or notebooks and as you said they are rather cheap nowadays (as long as it does not do bluray).
As I said when discussing it some months ago in another thread, if it was anywhere near prevalent, MS would be scrambling all its staff to fix it before its HQ got overrun by angry mobs with torches and pitchforks.
3. depends from what you need to save. I have double backups (one internal HDD one external HDD) plus critical stuff backed up on Dropbox, yet so far no HDD died on me (and even if it did I would notice and replace it before real data loss). IF you need to keep dozens of copies at different ages, then yeah, DVDs are the only possible route.