The transmissions are sealed from the factory but they can be checked by removing a cap and then you'll need a certain length flexible plastic stem to check the level. There is a thread on here somewhere that describes the procedure. If you've lost fluid through a leak (possibly the transmission connector) then the car can go into limp mode and exhibit many of these issues. It's always best to start with the simpliist thing to check, which would be for leaks and fluid level. I'm not saying it might not be something else, but............

Even if you have to take it to a tranny / dealer, you should have the fluid level and connector checked.

Best of luck. I hope it's something simple.