No, any priest who has the correct faculties can hear anyone’s confession. Having the faculty basically means that they haven’t been banned from hearing confessions by their own bishop/a local bishop/religious superior.
Are there ordinary and extraordinary ministers of Recociliation?
No. There is the priest only, there are no extraordinary ministers of Reconciliation. In danger of death, a priest who does not have the correct faculties can validly absolve sins, but this is the only sense in which there is an ‘extraordinary’ minister; the laity may never grant absolution.
Is there an obligation for confession if the person cannot physically go to confession?
There is only an obligation for confession in so far as one has committed a mortal sin. The physical capacities of an individual have no bearing on whether or not they must confess. If you mean a case where someone could not get to a church, then a priest could visit them at home (or wherever they were) to hear their confession. If you mean someone who e.g. could not speak, then special allowances could be made - an interpreter may be used if necessary, including a sign language interpreter, or they could use their usual method of communication e.g. writing things down, typing into a computer. They would still need to be physically present with the priest.
In terms of what Bookcat said, it is the custom for the Pope to choose a regular confessor, which is a useful thing for all penitents as it enables the priest to get to know us, our habitual sins and so on and so offer the best advice as to how to avoid sin in the future.