How to accurately determine mass transfer using balances?
Accurate weighing requires you to be aware of enormous amount of factors. It is not possible to cover them all in one answer. For starters, where do you put your balances? Are they levelled? Are there any heat or vibration sources nearby? Are there any sudden air flows? Is your mains power reliable? Were the balances calibrated properly? Is the ambient temperature or humidity too high or too low? Do they change much? Is there much static electricity (depends on the materials you are working with and on the ambient humidity)? Do you use gloves? How much do you weigh? I mean, not you weigh, but isn't it something less than the minimum weight requirement for your balances? Et cetera, et cetera.

Returning to your questions: in general, sensitive balances can handle large masses which are within the specification. However, the measurement uncertainty depends on the mass. Then, if the receiving flask is not perfectly flat, there should not be any problem unless the flask is wobbly or unsteady. The location where you put the flask should be as close to the center of the weighing pan as possible. It matters.

As for the other things you could do, I'd like to recommend you to check out some weighing practice manuals. You can start with the balances manufacturers - Mettler has brief Good Weighing Practice whitepapers, maybe others like Sartorius have something similar. Analytical chemistry handbooks should have something to offer. Then, check out the manual for your balances. Aren't you trying to weigh something more accurately than the accuracy of the balances (remember, accuracy $\ne$ resolution)? Then, if you don't, just ensure that you are following the recommended weighing practices as closely as humanly possible.