At the present time, I'm a little bit busy with my studies and job but, in my free time, I like to do several things. 

I like cook when I meet with my friends or family. I'm always trying to know learn new recipes and taste new flavours. Now I'm learning about the Indian cooking because I love the taste of the spices and the hot dressings. My friends know that and they are constantly saying to me, "Hey! When are you going to cook us that dish?" or "I found that recipe. When we are going to meet?"

Other thing that I'd would like to do is travel around the world, but I can't go to all places that I want because for this you need spend a lot of money. You need time to do that and, if you are working, you don't have time. If you have time and don't work, you don't have money...so when I've holidays and I have saved savings, I use that for travel.

Besides of all that, I like music, paint mockups and watch films and series.

For your last sentence, it does not sound right. If you have a list, you should write all of them the same way. There are two ways you can write it:

1) Verbs = I like listening to music, painting mockups, and watching films and series.

2) Nouns = I like music, paint, and films and series