Thank you in advance for your help!
re: "Would it be a problem if I re-install my OS and again enter my account and work through it?"
Upwork places no restrictions on the number of times you can re-install your operating system.
Upwork has no restrictions on the number of computers you can install the desktop time-tracker app onto, or the number of computers you can use to connect to Upwork.
I personally use many different computers and mobile devices to connect to Upwork.
This has never been a problem for me.
re: "And another thing - I'll be travelling to another country and will have to stay there for 2 months. Will I be able to work from there without this be considered as a violation?"
Upwork is not the "travel police."
Upwork places no restrictions on freelancers' travels.
Upwork does detect IP addresses and locations of where people are logging in from. If Upwork's automated algorithms flag an account as doing something problematic, then Upwork might look into it. Upwork might ask a user to do identity verification.
But none of these things are problems for honest freelancers such as yourself. Upwork's automated algorithms and security protocols are only meant to maintain a high-quality platform for all users. Part of this is detecting users with fraudulent identities and removing them from the platform. Upwork also looks for users who share their Upwork accounts with others, so it can terminate their accounts.
Regarding travel to other countries:
Upwork asks that users follow the rules and laws of wherever they are, and that includes work restrictions. But Upwork does not create those restrictions or advise users about specifics. Whether or not you are allowed to work in a specific place is up the laws of that place and your specifics, such as nationality, visa status, etc.
If you are travelling, you should NOT update the location on your Upwork profile.
Your Upwork profile location should reflect where you live.
If you travelled from Bulgaria to Romania for a week, then you would NOT change the location on your Upwork profile. If you moved from Bulgaria to Romania, then you WOULD change the location on your Upwork profile.