I am currently backing up my MacBook Pro late 2013 to a Time Machine. If something happens to my Mac (I can't use it anymore), can I retrieve my files and data onto another Mac? Thanks.
Yes that is exactly one of the reasons it's great to have a Time Machine backup.
With the new Mac, if you want to restore the data from the Time Machine backup, ensure it is connected to the new Mac. Then power on the new Mac and follow the setup instructions.
When you get to the question asking if you want to migrate data you would choose the option to do so from a Time Machine backup.
Choose the Time Machine drive (shows up as a green icon) and then click next. Choose what data you want to restore and then click next again.
For clarification and further information have a look at, Move your content to a new Mac and How to transfer backups from Time Machine to a new Mac.