I am trying to improve my English skills, but it i's more complicated than I expected. I am trying to improve my English skills, but it's more complicated than I expected.

Since you're writing causally, you can use contractions :) It keeps the casual flow of this text.

Anyway, I like watching movies and TV series. Anyway, I like watching movies and TV series.

This sentence is perfect, but since you're living in the U.S. I thought that I'd let you know that it's common for us Americans to say "show" instead of "series" You can use them both, but for some reason I always hear "Netflix show" or "this new show on Amazon Prime" as opposed to series. But, as said before, you CAN use both. So no stress :D

Anyways, I like watching movies and TV series. Anyways, I like watching movies and TV series.

These days, I’m watching How I Met Your Mother. These days, I’m watching How I Met Your Mother.

How I Met Your Mother should be italicized, since it's a TV show name. It's not super serious, but recommended, but I get that this can't be done on this website so no worries :D

Sometimes, we speak to each other in English, but it doesn’t last very long. Sometimes, we speak to each other in English, but it doesn’t last very long.

Just for flow :)

For all these reasons, I made a study schedule, and I am very determined to learn to speak English like a native speaker. For all these reasons, I made a study schedule and am very determined to learn to speak English like a native speaker.