Hello Wayne, welcome the wonderfully frustrating world of aikido
I would like ideas on things that I can do at home in between.
I don't know about your style/dojo but in ours we have a set of warm up exercises called aiki-taiso. They help teach basic body movements and most of ours relate directly to techniques that we do. If you can learn the aiki-taiso well it makes the techniques that much easier. A common phrase uttered with mock amazement in our dojo is "oh, it's just like the aiki-taiso" when sensei explains something and the student finally "gets it".
As for learning names of techniques I'd say give it time but then I'd be a hypocrite
I wanted to know what everything was called, right now! On my first day my sensei handed out a short lexicon of terms commonly used in aikido and our style/dojo specifically. I took it and made flash cards that I would carry with me to help me learn. I think the biggest thing that helped me learn the names of things was that I tried to learn the root words and then later strung them together. Example: katate (a single hand) dori (grab) irimi (entering) nage (throw). After I got a decent handle on the root words I would play a game of trying to decide what I would call a technique that sensei demonstrated. I was lucky to have a sensei who was patient and understanding. It didn't hurt that often it was just sensei and three of us newbies. I think he was just happy that we were interested
Hope this helps.