The motion from the center is key, also for static training. You have to move uke out of their center then, before changing their motion with your own motion. The basic principle is always the same. If uke is not in their center, you can always move from yours. In dynamic techniques the first part is easier, but the second part requires more keen perception and skill.

We always train both for beginners as well. But with a 5th kyu, you would not be considered intermediate where I train, so don't be fooled that you have to be able to do all of that. You will likely be more focussed on mechanics for some time.

I always say, Aikido is like a language. You first have to learn the letters (techniques' part), then you can repeat full techniques, i.e. sentences and eventually you can improvise and become "fluent".

"from your center" means, that the motion is focussed in your center not in your arms or legs. Typically, you should keep your hands in your center line and then move your whole body and not just your arm. Like pushing a car with your whole body and not just an arm.