Yes wiper motors have high torque and worm gear inside means free brakes if motor is stopped. Try to source a window/wiper motor of a big vehicle. The bigger the vehicle, the stronger motor manufacturer would have provided.
For simple dc motors (wiper, power window etc), motor driver is not an issue. You can make it yourself, or you can buy it from local electronics shop. Like here in rawalpindi, there are many electronics shops at college road. The techs there make all sort of circuits, you tell them this is my requirement and they do it for you. You can order online too. In my university times, we made the driver ourself using relays and transistors. It was a bi directional H-bridge with braking feature. Braking feature simply shorts the ground and + wire of motor together, this creates load on motor and provides resistance if motor is moved. You probably wont need it as wiper and power have worm gears and are self-locking.
Once you buy motors, find its stall current. Your driver should be able to handle twice this current. Relays are usually rated for high currents so dont worry but circuit should be made while keeping in view the current that might go through it.
For power design, you must first lay down your requirements. What is the run time are you expecting from batteries? How are you planning to charge them? Lipo is expensive but it has advantages you mentioned above. Since you want the chair to be mobile and fold-able, acid battery may not be the best choice. Consider the weight factor as well...
yes arduino uno is good for your application.
