Hi orxan,
First, since you already signed up on the Economist GMAT Tutor, I would highly recommend that you take advantage of the free online tutor session. You may be able to find great tips and strategies to improve your verbal skills.
As for SC, remember that the problems with SC questions rarely are only grammatical (though, be sure your grammatical skills are sound). You should always be sure you understand what meaning the original sentence is trying to convey. This will allow you to rule out answer choices that don’t make sense or violate the intended logic and meaning of the sentence.
For RC, I agree that you should continue reading publications. Also, if you don't already do so, take notes They will come in handy, especially for those long passages. Look out for these items while reading the passage: 1. the main idea of this passage 2. the author's position and tone (neutral? critical? etc.) and 3. structure of the argument (e.g. two opposing sides vs. one sided, informational vs. author's opinion).
Doing this will allow you to understand the passage and quickly identify what the specific arguments may be.
I hope this helps!
Jessica