Crunch, I think you mis-read. He has a hyundai, not honda. The Hyundai has a replaceable filter inside the pan. They use several styles of filter from the screen type to the Dacron filter. Lots of bolts to get the pan off and be careful because they break easily, apply a bit of pb blaster or something like that before you start. Use ONLY the recommended factory fluid, these guys are very sensitive to fluids and quirky at best. I do not recommend a flush as they tend to do more damage than help. Service it regularly, I recommend yearly.
As for the later shifts, these transmissions will delay shifts due to temp, outside and engine. You need to see if the engine is warming up properly, bad thermostat? You also need to verify what the temp sender is telling the pcm. If the computer thinks the engine is cold then it will delay shifts accordingly regardless of actual temp, a bad sending unit can do this.
Are there any codes? Post back, Transman