1) When I assign a Steward will they continue using whatever equipment I have them or will they resort to their default gear?

2) Also, if any of the animals I purchase die am I able to acquire a replacement?

3) Is there any particular Steward I should use for each manor/hall?

1) They re-equip their default gear, at least as of patch 1.8. 1.9 may change that.

2) Yes, you can buy another

3) Totally up to you.