Burgmuller has alot of great pieces that are musical, but excellent for beginner.
Having played only 9 months myself, taking lessons for maybe 6 of those, I have been playing Burgmuller from the beginning.
I still am trying to play several of the pieces you mentioned smoothly, and I can't do it yet.
Innocence is a good one to work on, has some chord changes that require fairly quick changes at speed. La Candeur is another one which is similar in nature for chords and movements of the hand.
As mentioned by others, treble clef when it appears on the bass line means you play those notes with the left hand. Remember, above Middle C, because that is where the Grand Staff meets and hands are divided generally. Burgmuller has several pieces, like the ones above, that ask for this.
Some other suggestions about relaxation others have made are good, and you have been reading over Chang's book. Pick out the important stuff of his work, like relaxation, and eventually learning thumb over, and other theories he presents. You can easily get lost in "science" and the main points with his work, it is a bit wordy for me.
I would also slow the pieces way down and clearly hit all the notes and slowly build speed and work out the technique for movements while doing this hands seperately, then get working towards hand together. There is not one perfect way for you to bring your hands up, position fingers, bring hand back down. It takes a long time, especially if you are older like myself, to build speed and accuracy. It is something you have to wire your brain to do and learn via muscle memory.
I can move faster than full speed with Arabesque, not smooth and as clear as I would like, but working out technique, hand movements etc..while building speed would help.
I guess this is where somebody who understands good hands movements and things to practice to help with this issues you are having can be useful, finding a good teacher isn't easy though that knows these learning methods.
I think you might be exaggerating your forearm rotation according to you last post. Anotehr thing to do, get video of very good painist that show their hands, forearms etc..well. I don't think you will pick up on alot of forearm movement, it is subtle, but can be beneficial when used properly. So that test you tried at your keyboard might not be a very good representation of what actually happens and is required to play piano, somebody correct me if I am wrong on that, I am sure you will knowing this board.
I also started on a keyboard, you may have a yamaha that plays the music you are referring to? This is what I had, it is good to hear it that way and watch the notes and use that with the written music. But you also need to have a good basic music theory knowledge to understand what you are looking at.
I eventually got a piano and the keyboard sits in the garage now. I would say you can't get good muscle/finger strength from a keyboard and transfer that to a piano, the feel is definitely different. But my father who has played strickly keyboard since he was young, can sit on a piano and play fine, so I think if you plan to just play piano, and can afford a descent used upright even and have the space, it is more motivating.
Sorry a bit lengthy of a response, but I tried to address several posts here you had.
All I can say, is it takes time, and you have to learn how to apply certain good principles to yourself if you are not working with a good teacher, everyone is different. I recommend you search for "Bernhard" and his useful posts which are similar to Chang. Bernhard is more direct to the point with his methods, search the site for his name and you will find alot of good stuff to apply to your learning.
Good luck.
Topic: Arabesque Confuses Me...