As a non-EU migrant it's really hard to deal with a bunch of unsolved problems that you have to tackle durwhen facing a tight deadline. As a non-EU migrant it's really hard to deal with a bunch of unsolved problems that you have to tackle when facing a tight deadline.

its = belonging to it it's = contraction of "it is" (common mistake for native speakers too)

As a non-EU migrant it's really hard to deal with a bunch of unsolved problems that you have to tackle duringon a tight deadline. As a non-EU migrant it's really hard to deal with a bunch of unsolved problems that you have to tackle on a tight deadline.

Using "on a tight deadline" sounds more natural.

I believe that the most critical one is the job hunting process. I believe that the most critical one is the job hunting process.

This does make perfect sense another simpler alternative would be: > I believe that the most critical one is finding a job.

In the hope that eventually I will convince a company to hire me and acceptgree to become my VISA sponsor, so it will be a guarantee for me to preserve everything I have built abroad so far. In the hope that eventually I will convince a company to hire me and agree to become my VISA sponsor, so it will be a guarantee for me to preserve everything I have built abroad so far.

"accept to become" is gramatically incorrect. You could use "agree to become" (I prefer this one, it's more active and positive) or "accept becoming" (this has a more passive undertone, like they are putting up with something slightly negative)

In the hope that eventually I will convince a company to hire me and accept to become my VISA sponsor, so it will be a guarantee for me tohe preserveation of everything I have built abroad so far. In the hope that eventually I will convince a company to hire me and accept to become my VISA sponsor, so it will guarantee the preservation of everything I have built abroad so far.

"guarantee the preservation" sounds more natural to me, but what you said did make perfect sense.

I am attempting to achieve better communication and presentation skills, as well as extend my network and social bonds with locals. I am attempting to achieve better communication and presentation skills, as well as extend my network and social bonds with locals.

As it's a continuous action the "present continuous tense" makes more sense and sounds more natural.

I'm attempting to achieve better communication and presentation skills, as well as extend my network and social bonds with locals. I'm attempting to achieve better communication and presentation skills, as well as extend my network and social bonds with locals.

This is a specific ongoing action at the moment, rather than just a general action that's always true (e.g. I brush my teeth each morning), so this tense works better.