Can you practice and improve physical activities only by thinking? By physical activities I mean any kind of task, work, sport, you have to use your body. 

Not always have the time to do some task or even the possibility (need some equipment, not great situation). I try to imagine myself doing what I intend to practice. Example: some katas (karate movements), sign language, arts&amp;crafts. Is like I imagine how will it be so when I can do it, I can do it better. 

Do I need to practce the real movements to improve or by thinking I have enough?
Yes. In one famous experiment,a college basketball team was divided into three groups.

Group 1 was supposed to show up to practice shooting baskets for a week on a daily basis.

Group 2 was asked to "think about" practicing shooting baskets during the alloted time, without showing up.

Group 3 was asked to "forget about" basketball for the week.

After the one week period, Group 3 showed no improvement in shooting baskets. 

Group 1 improved meaningfully.

Group 2 improved almost as much as group 1, and way more than group 3.