Time machine and Mac repair
Yes, Time Machine should restore all your applications, personal files, and preferences, provided you have not made any files private the Time Machine system preferences pane.

When you get your new Mac (or freshly installed OS), it will ask if you want to restore from a Time Machine backup, and I think the process is self-explanatory from there.

One caveat - if you have partitioned your hard drive, I believe only the first partition will be automatically restored. You'll have to manually restore the others.