I really like these Burgmuller studies...I just started The Little Party yesterday. The tempo for The Farewell seems incredibly fast (quarter notes at MM 184

) but I think you could try to play at this tempo using a few tricks before deciding to slow it down. Try this fingering, from the Schirmer edition:
3 2 3 4 5 4 3 4 3 2 3 4 | 5 3 1 4 5 4 3 4 3 2 3 4
C A C D E D C D C B C D | E C A D E D C D C B C D
Before playing it on the piano, just drum this fingering on the table, slowly, then speeding up to as fast as you can. Also, drum your fingers in the pattern of just the transitions between the triplets - C D E, E D C, C B C etc. - using the same fingering.
Now, try it on the piano! It helps to have a really relaxed wrist and forearm and to keep your fingertips touching the keys.
BTW, the 4th and 5th fingers are weaker than the others by design. But I bet doing studies like this one is the best way to improve their strength and coordination.
Hope this helps!