No, that sounds awkward. Depending, I would say "My fluency in English..." or "My English is improving" or "My knowledge of English is..." If you could be more specific as to context, I might be able to help you more.

You can put your phrase in quotation marks and search for it. Unfortunately, all the results point back to this question, so the answer is clearly no. You can say "my control of English" to mean how well you manage speaking the language. Please remember that "English" always has a capital E. This is not optional.

You need the word "proficiency", not "possesion". In Russian it is the same word "владение", but in English it isn't. You can say "my English proficiency level", or "my level of proficiency in English", or simply say "my English".

Interestingly, at least to me, is that you can say "My grasp of English vocabulary...."