Escape from Back Take
To escape from a back take when your partner has their hooks in and seatbelt grip, prioritize protecting your neck by defending their choking arm (overhook) with your opposite hand. Keep your elbows close to your body as you do so. Fight their hand with a 2-on-1 grip, maintaining the defense as you rotate to their underhook side, bringing your head and shoulders to the mat while turning into them. You can peel off their hook with your hand, but be careful not to get into the straight jacket position. A safer option is to switch your hip outward, bringing your butt to the mat.
Escape from Armbar
The Hitchhiker Method
In the late stage of armbar defense, when your arm is stretched out and you have both their legs across your head and chest, rotate your elbow and “answer the phone” by hugging their thigh. Walk your body in a circular motion away from them (while turning your face into them), continuing until you feel your arm is no longer in danger. Then, stack them and pass their guard.
The Second Method
This is a bit earlier in the armbar defense, when you are crossing your arm to prevent your partner from peeling off your grips. In order to straighten your arm, they have to remove their top leg (the leg above your face). Seize the opportunity, catch the top leg, and bring both of their legs to your hip. Posture up and turn away from them. It helps if you relax your arm and yank them out of the grip; you should escape then.
Notes
While these escapes would be more effective in no-gi due to the slipperiness, they can be less productive in gi due to collar grips and friction.