I work primarily outpatient in community psychiatry, though I have also worked at a crisis facility and do some inpatient rounding PRN. There are a number of specialties in psych which are quite different from the kind of work I do (e.g. substance abuse, working with TBI or HIV patients, crisis work, mobile outreach or ACT teams, eating disorders, liaison work in hospitals [which is very interesting if inpatient and medical comorbidities are your thing]). Psych has much broader applications than most people realize, though you must always be mindful of your scope of practice.
I currently work 8-5, M-F. I'm on call 4 days out of every 3 months unless I want to pick up more, and I am compensated well for it ($300 a night for F/Sat/Sun call and $125 a night for weekday).
I do not do any counseling, but I DO do psychoeducation, try to throw in some basics of CBT, talk about engaging with group therapy, etc. Unfortunately, employer does not want me doing therapy, as that can be farmed out to the LPCs and LCSWs. I have a caseload of over 1,000 patients and have only 20 minute appointments, so I feel like a conveyer belt towards a prescription pad at times. However, you can still make a big difference even given 20 minutes... meds aren't miracles for most people, but I've seen some amazing changes which make the work seem very much worth it.
As far as what I see patient-wise, it depends. I've worked at a few different facilities; at my current position, I have mostly stable patients... however, I am occasionally floated to cover for other prescribers, and the NPs who work at our crisis facility and on mobile crisis team frequently have medically and psychiatrically ill patients. When I was in Seattle, I worked with forensic and supportive housing clients who were about as medically and psychiatrically ill as they come. All this business about NPs don't take sick patients, the MDs take those-- very much NOT true in psych. If anything, I had patients who were quite a bit more ill than what most of the MD colleagues had.
As for the money, a lot of it is how shrewd a businessperson you are. I can't speak for other specialties, but I personally would not take a job as a psych NP in a major market for less than $90k a year. You have to negotiate with employers and insurance companies. A lot of nurses and NPs are not good at this, which is probably part of the reason our wages are generally lower than they should be.