Our outside unit blows cool air out with the compressor seemingly not working - then the compresser kicks in and hot air comes out of the unit. What's going on with the unit? Is it about to totally die on us?

Feel the lines coming out of the compressor. One should be hot, the other cold. Some units don't kick on, right away... they have a delay from when the fan kicks on, and when the compressor does. How long does it take for the compressor to activate? Does your unit blow cool air, once the compressor does kick in?