Automatic Chrysler Neon Transmission 97

Hello friends at the mechanics manuals forum, how are you? I need some help with my '97 Neon. I'm new to mechanics... The problem is that the automatic transmission is malfunctioning. When the car is cold and I try to put it in reverse, it doesn't engage, and I have to accelerate several times before it does. I've also noticed that when I'm starting, first gear works fine, second gear takes a little while to engage but then shifts into reverse, and third gear takes even longer and the RPMs increase significantly. After the car is fully warmed up, it works "fine." Reverse engages immediately, and forward works fine, but third gear takes a long time to engage. I'd like to know if you can help me with this problem...

Oh, another thing, the car seems to have some other issue. I've only had it for four months, and I've noticed that it doesn't warm up when I start it. You're supposed to let "vehicles" warm up so the systems can work properly, but mine only gets hot after driving at least 8 km. What could be causing this?

Thanks, I hope for a quick response.