For a moment, disregard risks/feasibility/costs.

Yes, the critical path can be reduced, BUT doing so would render it non-critical and some other path will become critical.

Activities on the critical path have zero float. Hence it is a sensitive path and messing with it can have undesirable effects.

Yes, crashing or fast tracking can be applied on the critical path, subject to the above mentioned conditions.

The critical path is structurally no different than any other network path; it just has the longest duration and zero float, making it critical/crucial/important as it defines the project duration.

Regards.