Trap, Skeet and the 20 Gauge- Any Hope?

[Virginian]

That is typically a very nice handling gun. With that gun combo you ought to be okay at trap as long as you don't try handicap shooting - i.e. shooting from further back. Remington 870s have probably broken more clay pigeons at trap than most everything else put together.
For skeet you need a much more open choke. 20 gauges do almost as well, and I mean within a tenth of a percentage point, as 12 gauges at skeet. Starting out you may be at a slight handicap with a pump versus a semi auto or double barrel on the doubles, but you will learn. I've shot a many a 25 with a pump.
If you want to get serious at skeet you need to get your barrel fitted for choke tubes, or get another barrel. Interestingly, I have 12s and a 28 with choke tubes, but my 20 gauge 1100 has 3 different fixed choke barrels. Full 3", Full, and Skeet.