To note. I replaced the selenoid,because i thought this was an issue that was causing my battery to constantly fail. Looking back,I see that that was not the case,but it was. The selenoid was no bad,just miswired. I rewired the selenoid in the same configuration as when i took the old one off. That is what the issue was to begin with. Since the selenoid was wired incorrectly would it cause any of the following issues?

Battery not charging
Engine running hot
But also,if it was incorrectly wired from the beginning,would it not have had the same problem of not cutting off the engine as before? The only thing that i heard from the motor was a constant humming after turning off the ignition which sounded like a fan. Leading me to believe the engine had overheated,although the temp guage did not indicate this. Maybe because it doensn't work either.