From your original post you said the fuse was blowing when the engine was running
SO what I would like you to do is fully charge the battery then go mow with the rectifier plug off.
Before you start spending your hard earned cash we would like to find the problem
No good replacing expensive parts if all that was needed was 2" of tape to cover a chaffed wire
Hopefully the mower will run for the full capacity of the battery which you can calculate ( roughly) by dividing the Ah number by 5 .
Depending upon the battery used and it's condition you should get at least 50 starts or 5 hours mowing out of it before it gets too flat to run the mower .