3) Would the maximum torque of each servo depend on the 'number of servos' I use? ..i.e. the power provided to each servo?
Each model servo has it's own maximum torque specification. You must purchase the servos strong enough for the mechanical loads you will be giving them. And your power source must be able to supply the maximum current draw for all the servos combined. Plan on large expensive batteries, but battery selection can happen later while you build and prototype your project perhaps using AC powered DC output power supplies. Modified PC power supplies are an inexpensive source of DC power while designing, building, and testing projects.
I would have to respectfully disagree with selecting the batteries after getting something working without batteries, especially a robot. Really, they should be selected as part of the design phase, if at all possible. You might need to do some test chassis runs or other experimentation to see what kind of torque vs. weight vs. current consumption is needed, then carefully design your chassis so that when you put on the selected battery, it works out properly.
See, the problem is you can get into this weird "vicious circle" where you need more current for more run time, but that drives up the weight, which requires more torque to move, which requires stronger (and possibly larger) servos, which require more current, which require bigger batters, which drive up the weight, which...
I think you get the picture.
The only way around this is to plan around it as early as possible - so you know what kind of battery technologies you can use for the run time, weight, torque and current requirements, etc in the final design.
/definitely not an easy way to solve this problem, on any robot - let alone a stair-climbing device...