several questions (tensions)

I suppose you refer to tension in a rope (o string, or cable).

At equilibrium, physics law tells us that all forces balance each other. The tension along a rope is therefore remains the same throughout. If not, the string would either stretch further or shrink until the tension becomes uniform.

There is example in which the tension along a rope is not uniform. Consider a heavy rope that hangs vertically at one end. Due to the mass of the rope, the tension at the upper end of the rope is somewhat higher than that at the lower end. In other words, tension decreases when going vertically down the rope.

2012-01-30 16:34:08 補充：
Your suppl questions:
As explained above, the tension along the rope is constant throughout. If not, the rope will elongate or contract until the tension is equal.

2012-01-30 16:40:58 補充：
(cont'd)... Suppose the left group of people exert a force (F1, say) on the rope larger than that exerted by the right group (F2, say), then the tension T along the rope is somewhat in between, i.e. F1 > T > F2.

2012-01-30 16:41:15 補充：
(cont'd)... Under such situation, the left group of people experience a net-force (F1 - T) towards the left, whereas the right group of people also feel a net force (T - F2) pulling them towards the left. Thus, the system (i.e. all players) moves towards the left.

Yes, the tension'll be equal even though there are different forces applied on both sides :)