You got 2 options...replace the lug on the end of the battery cable or replace the whole cable. Every time you clean the posts you remove a little lead from both parts till they don't have a good fit anymore. Once you have a solid connection to the terminals I bet the other issues will go away, fix the cable first and see what happens.
l We're here for a good time. Not a long time. So have a good time the sun can't shine every day.