How to improve the language of my master thesis by myself?

My best tip for proof reading your own work is to have your computer read it back to you. We often notice how things sound weird when they are spoken compared to when they are written.

Microsoft word includes text-to-speech as part of the Word. I use it all the time. Stand alone text-to-speech software is available if you use something else for your writing.

I suggest you seriously consider contracting the services of a native English speaker who's also either an academic or has some professional writing or editing experience (literary or academic). You don't write degree theses many times in your life - typically once for your Master's, then again for your Ph.D.; so it's worth it, in my opinion, to make this investment. Not only will this make your thesis more pleasent to follow, it may also improve the clarity for your official academic readers / exam committee; and the corrections you receive will serve you well in your future academic authorship.

If you had more time on your hands, I'd suggest working on improving your English writing skills; as @RichardErickson notes, many universities offer such services to graduate courses, sometimes as proper semesterial courses, sometimes on a less formal basis. There are also resources like Strunk & White's Elements of Style booklet which, if taken to heart and applied to your thesis, will also be very helpful.

Finally - and perhaps most importantly - I would also consider asking colleagues of yours to have a look at your thesis draft, to make sure they can figure out the contents more than to give you feedback about your English.

You seem to have a mistaken view of what constitutes plagiarism. The choice of an individual word or trite phrase, such as "as demonstrated in the figure," or "a careful analysis shows that" cannot be plagiarism. The reason for this is because such behavior does not meet the primary criterion of plagiarism, which is the misappropriation of someone else's intellectual work without credit. Even using someone else's term for something is not plagiarism. (For example, it is not plagiarism to use a word like anomie or superego just because someone else came up with it!) Similarly, grammar checkers such as Grammarly or a built-in word processor feature only offer suggestions for how to fix errors in your writing. Accepting their suggestions is no more plagiarism than working with a professional proofreader.

However, another suggestion for how to handle the proofreading would be to find someone who is a better writer and speaker of English than you are to help you with the proofreading, as we often tend to be too close to the writing, particularly if it's something that we are in the middle of working on intensely. Somebody else's judgment will help far more than trying to do it all yourself.