Hi Ariadna,
I'll try to answer your questions:
1.- I'm afraid that's right, but assuming all your subjects are acquired with the same acquisition, you only should check it once. I know mrtrix provides a tool called dwigradcheck that can be useful for this, also DTI studio has his own gradient checker, but I always check it visually.
2.- You can do it before eddy. Eddy will modify the orientations a little bit, but if something is really wrong (an axis flipping for example) it will be clear before eddy as well.
3.- In all my pipelines I never do brain extraction per se, I use the mask for topup and eddy, and then I calculate it again after that, but I nevver mask the diffusion image.
I hope this helps.
Best regards,
Manuel