Since the other expert never got back to you I will answer your question.
If the transmission fluid is full, checking it in park at idle then the following applies.
Sorry to say that I have seen too many of these problems with your symtoms and codes. I am afraid your transmission has to be either rebuilt or replaced. I would shop around for prices.
P0734 is incorrect gear ratio in 4th gear. meaning it is slipping in that gear.
P0740 is torque converter clutch problem.
P1624 Mil request, TCM to ECM. Meaning the trans computer is telling the engine computer it is not happy.
P1500 Vehicle speed sensor problem. Probably due to slippage.
P0171 Ignore that for now unless your engine is not running properly. If you have engine problems correct them first before spending money on the transmission. A poorly running engine will affect the operation of a transmission.
By having to rev up the engine to get it into gear means there is an internal pressure lose due to aging internal pressure seals.
Sorry for the bad report.
Feel free to get back to me.