1lb/450g tins of vegetables or soup make good hand weights for arm exercises. So do hand-size bottles or cans of soft drink. (Don't open them immediately after use.) Holding the weight in each hand at your sides, alternately raise each arm to shoulder level.
Squeeze a tennis ball or tightly rolled up pair of socks in each hand to strengthen your grip.
To stretch your calves, sit on the floor with your legs straight, loop a bath towel around the ball of one foot, and pull, resisting with your foot; repeat with the other foot.
For ankle weights, fill socks with dry sand, dry rice, dried lentils or beans, or clean cat litter. Weigh them (start with 2lb/900g) and tie them shut, leaving enough room in the toe to fasten the weight round your ankles. Lie on your back, with one knee bent and the other leg straight, making sure your lower back is flat on the floor. Raise the straight leg as high as you can. Switch the position of both legs and repeat.
Stand, holding a towel above your head, and pull on the ends so that you bend sideways at the waist. Repeat, bending the other way. Don't lean back or forward as you bend.
Rest your ankle on the back of a chair at hip height, keeping the leg straight. Bend forward, getting your face as close to your knee and your hands as close to your ankle as possible; hold for 5 seconds. Repeat with the other leg.
If you're not doing somersaults, a bath or beach towel on a rug or a folded cotton or wool blanket will work just fine as an exercise mat.
Or exercise on a firm mattress, preferably one resting on a bed board, a platform bed or the floor.