Hi Sophie
The best alternative for you for abdominal work would be to do the exercises on a Swiss ball. However, if you don't have one, you can always do something like standing rotations (stand with feet together then crunch elbow to opposite knee, then switch sides) or plank, or superman (on the knees, not flat on the stomach).
For bingo wings - you can build the tricep muscle, but you can't target fat loss - as you lose weight some of the fat will come from the arm naturally. If you want to work your triceps you can do tricep pressups, tricep extensions or tricep dips.
I'm happy to describe any of these exercises if you don't know what they are.
I don't have a gym membership but the gyms around here range from £25 a month to £55 depending on the facilities. At some of them you have to pay extra for certain stuff like sauna or squash courts.