By definition, a Catholic chaplain is a priest. A deacon, religious sister or brother, or lay man or woman can be a “spiritual worker,” as it were, in hospital or prison ministry or military service, but is outside the strict definition of “chaplain.”
Not true. Most Catholic hospitals employ chaplains for their Catholic patients who are not priests. There are large national organizations approved by the USCCB like this. So, no, hospital chaplaincy is not provided solely by priests and neither are all hospital chaplains priests.
Here is one of the larger organizations for example: http://www.nacc.org/aboutnacc/history.asp