1. Are bighats in fashion now? (в моде ли нынче широкополые шляпы)
2. Nobody wears wide belts. Are they out of fashion (старомодные)
3. I often put on my favourite old jumper. (надевать)
4. Tom took off his boots and socks and came into the water (снимать обувь)
5. Do you know what coats are in fashion and what coasts are not in fashion
6. First he put down his cap and then took it again (скорее всего здесь подходит put down (положил) то есть, он сперва положил свой головной убор, а затем вновь взял его).