On the surface it sounds like your transmission fluid is either low or completely exhausted; have you checked it recently?
Regarding changing the transmission for a manual, yes, it can be done, but it is not for the faint of heart or the light of wallet; swapping the transmission is the least of your worries, messing around with the ECU and wiring harness, the dashboard changes, the mounting of a clutch pedal, and of course swapping out the console and mounting up the shifter mechanism can take weeks for an experience mechanic and months or longer for an inexperienced individual.
Long story short, fix what you've got, that will be the most cost effective solution.
Regarding changing the transmission for a manual, yes, it can be done, but it is not for the faint of heart or the light of wallet; swapping the transmission is the least of your worries, messing around with the ECU and wiring harness, the dashboard changes, the mounting of a clutch pedal, and of course swapping out the console and mounting up the shifter mechanism can take weeks for an experience mechanic and months or longer for an inexperienced individual.
Long story short, fix what you've got, that will be the most cost effective solution.