When do we say that work is done?

Justify giving proper reasoning whether the work done in the following case is positive or negative: Work done by a man in lifting a bucket out of a well by means of a rope tied to the bucket.

Does work done depend upon the velocity of the body?

Does the transfer of energy take place when you push a huge rock with all your might and fail to move it? Where is the energy you spend going?

Given below are a few situations. Study them and state in which of the given cases work is said to be done. Give a reason for your answer:
$(i)$ $A$ person pushing hard a huge rock,but the rock does not move.
$(ii)$ $A$ bullock pulling a cart up to $1 \, km$ on the road.
$(iii)$ $A$ girl pulling a trolley for about $2 \, m$ distance.
$(iv)$ $A$ person standing with a heavy bag on his head.

In case of negative work,the angle between the force and displacement is: (in $^o$)