I’ve been studying and increasingly practicing my eEnglish for many years now.

I learn and improve it by watching films, series or just by speaking to other people.

I’ve been studying and increasingly practicing my english more and more for many years now.

having increasingly before the verb sounds a bit clunky

I’ve been studying and increasingly practicsing my eEnglish for many years now.

“English” is capitalized.
Typically (at least in British English) “practice” is a noun and “practise” a verb.

Hello, everyone.

A period sounds strange. Normally you would either place a comma in the middle or at the end, as in one of the other corrections, or you would use an exclamation mark.

I’ve been studying and increasingly practicing my eEnglish more and more for many years now.

I learn and improve it by watching films, and television series or just by speaking to other people.

The parallelism here was wrong. It was set up as “watching X, Y, Z” when you wrote “watching movies, [TV] series…” but it was broken up when you wrote “speaking to other people.” You can fix it either by combining “films” and “TV series” or by adding a new verb to “TV series.”

English is very much included in my everyday life and that’s exactly why I’m trying to become even better at speaking it.

Greetings

Placing this at the end of a message comes across as odd.

Hello everyone.,

If you were writing a letter, you'd use the comma "," after the greeting.

I’ve been studying and increasingly practicing my eEnglish for many years now.

I removed "and increasingly practicing my" because it makes the sentence a lot simpler and clearer.

"increasingly practicing" doesn't sound right to my native (US) ears. If you meant something like "I've been practicing more and more lately" that would make more sense. But I'm not sure if that's what you meant.

"my English" also doesn't sound right in this context...though "my English" is correct in other sentences, see below.

I learn and improve itmy English by watching films, series, or just by speaking to other people.

"my English" sounds right here instead of "it". And I added the Oxford Comma. ;)

English is very much included ina big part of my everyday life, and that’s exactly why I’m trying to become even better at speaking itimprove my spoken English.

This sounds a little more natural to my ears. "improve my spoken English" is a little more formal than "be a better English speaker", which you could also use.

GreetingsBest regards, ¶
¶
<your name>

We never say "greetings" at the end in English. So some other sign off, like "best regards", or "with love", or "yours truly" works better here.