I've been studying English byusing mobile apps. I've been studying English using mobile apps.

or "with mobile apps"

I've been studying English by using mobile apps. I've been studying English by using mobile apps.

I've been studying English byfrom/via mobile apps. I've been studying English from/via mobile apps.

But I have the impression that these apps aren't pushing me forward to improve my English. But I have the impression that these apps aren't pushing me to improve my English.

Another verb that you could use instead of "pushing" is "motivating"

But I haveget the impression that these apps aren't pushing me forward to improve my English forward. But I get the impression that these apps aren't pushing my English forward.

"pushing me forward to improve my English" means that they're not motivating you to improve your English. I think you mean that apps aren't improving your English directly. I don't think you mean the apps aren't pushing you. It's subtle but "you" and "you're English" aren't the same. You want your English skill pushed forward, not yourself here (I think).

But I have the impression that these apps aren't pushing me forwardenough to improve my English. But I have the impression that these apps aren't pushing me enough to improve my English.

I guess that writing this text, is pushing me forward to improve my English, because it is a little uncomfortable tofor me to write this text. I guess that writing this text is pushing me to improve my English, because it is a little uncomfortable for me to write this.

I guess that writing this text, is pushing me forward to improve my English because it is a little uncomfortable tofor me to write this text. I guess that writing this text, is pushing me to improve my English because it is a little uncomfortable for me to write this text.

Same as above - this sentence isn't wrong, but I think you mean that writing this text is helping push your English skill forward, not put yourself forward. You can push yourself to write more often. Doing that writing pushes your English skill forward.

I guess that writing this text, is pushing me forward to improve my English because it is/ it’s a little uncomfortable to me to write this text. I guess that writing this text, is pushing me forward to improve my English because it is/ it’s a little uncomfortable to me to write this text.