which is faster( int or char ) ?

Sign: Definitely unsigned because a true value must be always bigger than a false value by definition. If false is zero, then true shouldn't be negative.

Type: I think there is no good answer to this question. The answer is dependent on the architecture and the compiler in use plus a lot of other factors (where do you use it and how): for example in a bool array a char might be better because a cache line can hold more items if you iterate over the array, but on the other hand in a packed struct an int might be better because it wont screw up the alignment of the next member in the struct... And we could give similar pros and contras for each solution. The C++ bool is 1 byte, and the C winapi uses a BOOL that is defined as follows:
typedef long BOOL;

My answer: choose whatever width you like, but I would stick to unsigned for the reason I mentioned above.

You should consider switching to .cpp source files from .c if its possible. I'm not kidding. Even if you write your source in C style without object oriented constructs you get some benefits! You have a bool type immediately, can declare your variables anywhere inside a function, name mangling prevents linking of incompatible functions/function users, you can use C++ classes/smart pointers/containers even without serious C++ knowledge, ...

It depends, which one uses the same number of bits as your processor/OS? For example, on a 64-bit system with a 64-bit OS, your best option is probably the data type that is 64-bit. Realistically though, you'll probably get the same performance with anything smaller than that as well.