1. The FNP program doesn't prepare you for acute care (you will see some who will tell you that they did all of their clinicals in a hospital setting). The certificate program is the NP specialty portion that focuses on acute care. It qualifies you for certification in a new specialty. You just don't have to repeat a lot of the graduate core courses like research, pharm, patho, etc. If you are really interested in working acute care, do an acute care program from the start. If two new grads are applying to a hospitalist position, one FNP and one AGACNP, who would you hire?
2. Depends on the state. In my state (which has strictly enforced the role portion of the consensus model), an FNP absolutely cannot care for acute patients regardless of the setting. Not only can you not get hired, but they've forced FNPs that have been working those roles before to go back to school and get certified in acute care or leave the job. In other states, they don't enforce roles so strictly so you'll see FNPs all up in acute care.
Being an ACNP doesn't mean you can't work outpatient at all. They can also be found in outpatient specialties. This might mean that you have clinic hours and hospital rounding. You could also look at some of the "emergency" dual track programs. Although emergency might not be your goal, they are typically an FNP and AGACNP program rolled into one and would prepare you to provide primary care and acute care.