I have read that Adobe flash player will cause my macbook to overheat
That might have been true for the 13" Intel HD 3000 graphics models, but the newer machines with Intel HD 4000 have a bit more kick in the CPU graphics.
and a bunch of other rumors. is there any proof or truth that Adobe flash player is bad for my macbook pro?
No it's not bad, it's just that the late Steve Jobs came out publicly against Flash because it couldn't run on the new low performance devices like iPads and iPhones that he was serving up.
So a lot of young people took it as a mission to kill Flash and bad mouth it to death.
What you do have to do, like you need to do with any browser plug-in or software, is be careful from where you install it from as there are many websites that will try to trick one into installing a fake one.
Many people thus tricked into installing a trojan immediately blame Flash as the cause, when it's not.
Also you have to keep it updated, but using a browser like Chrome will do it for you and Firefox will not let you run outdated web browser plugins.
Safari also blocks outdated plugins, but Apple is very slow to issue updates so it's almost worthless.