Seriously monitoring this thread.. I honestly have no idea what kind of exercises to do work out my back, and for my legs I've always just done the leg press :
For triceps I've always put one knee on a bench, other foot flat on floor, fist facing the floor and pulled the weight straight up, is this right?? I know you can stand and hold the weight by your side and lift it backwards, also right?
What you explained here sounds like a bent-over row, which works your lats (mid-back). A slight change would turn it into a tricep exercise, though. Hold the weight up so that your arm makes a 90 degree angle, with your bicep parallel to your torso and forearm perpendicular to your torso, and then straight your arm out, bringing the weight behind you. However, I'm personally not a fan of these lol I think skull crushers and tricep press downs (on cables) feel much more effective.
As for your back, there's a lot of different things you can do. For upper back, I like to do back flies. You can do them with dumbbells either standing up and bending over (which adds challenge to your core!) or on a bench, positioned with your chest against the bench, or you can sometimes do them on a chest fly machine but just sit on it backwards. This doesn't always work though, depending on the design of the machine. You can also do a machine or cable row using a wide grip bar, keeping your elbows high to be approximately in line with your shoulders.
If you do a machine row with the standard narrow grip and your elbows down by your sides, this will work your lats. These can also be done as you described earlier, with a dumbbell and a bench. You should also do lat pull downs and pull ups, with a wide overhand grip. A chin up with a narrow underhand grip will work mostly your biceps, which you can do if that's what you want, but a lot of people do them thinking it's for their back. Pull ups with the overhand grip are a lot harder, but a hard exercise means it works better! And there's no shame in using the assisted pull up machine if you need, I use them all the time. Full body weight pull ups tire me out too fast to get a satisfying number of sets in.
And finally for your lower back, the best is deadlifts, but be sure to check videos on how to do them or get someone to teach you, it's very important to keep your spine straight on them. You can also do spine extensions, which is done on this apparatus that holds you horizontally by the feet.
I could try to explain in better detail how to do these but I feel like this post is already long as it is!