No need for an amp to work on your fingering exercises, and or coordination between right and left hands. In fact, it may be better working without an amp for that. That said, anything that deals with dynamics, an amp is essential.
Strongly disagree. The whole entire point of left-hand and right-hand technique is to produce a good, musical tone. If you can't hear whether you sound good or bad, then how do you know you are developing good technique?
A specific example is muting. It's impossible to tell whether your muting technique is good or bad if your bass isn't plugged in.