Hello there! Here is a break down of the majority of the codes you posted and an explanation.
First of al the P1402 + P1403+ P0441 are all connected.
P1402- DMTL Motor Circuit
P1403- DMTL Valve
P0441- Gross evaportive emissons leak (of the least concern of all codes)
are both in connection with the Charcoal canister. Generally over fueling a vehicle cause these codes. Hyundai's are particular prone to this issue due to emissons control locations. Simply put a DTML is a sensor. There is 2 of these particular ones on your car. One mounted at the engine and one connected to the throttle body. Fuel more than likely has contaminated the charcoal canister. If only one of the codes were set i'd assume it was just a wiring issue. More than likely the canister and solonoid need to be replaced. Obviously checking the wiring should be done first. Corrison or a broken wire also could cause these codes to trip.
Transmission Temp Pull-Up Resistor issue. I am not a Hyundai Tech so I don't have allot of experiance with there transmisson codes. However the same code with same function is listed on the F-body site(GM). I would correct the other 3 and go from there. I assure you that poor engine performance would definately cause transmisson issues, especially with the shift points. Especially with a transmisson like yours that is totally electrically controlled. Please let me know if any of this makes more sense. If need be I can elborate more.