Your symptoms (well at least your tablets symptoms) point towards a battery which is faulty. Usually, when a battery gets hot while trying to charge normally, and provided you have got the correct charger, that means it may have developed a high internal resistance and is possibly shorting out somewhere internally. I would seriously think about getting it looked at and/or changed, before it goes much further. Lithium batteries used in most battery operated electronic appliances can suffer what's known as a catastrophic failure and have been known to even burst into flames, so be careful and get it seen to asap...
Sorry to sound alarming but be on the safe side first,, AND remember,, this is only my opinion...
Al