Hi
1. If through amazon I will sell my items to the EU, am I correct in understanding that it's Amazon's responsibility as OMP to deal with export/import VAT's and I as VAT unregistered seller don't need to do anything about it?
You need to check with the party who will handle the shipments, if it is Amazon handling the shipments please check with them.
2. For the scenario from point n1 above, my customers won't be charged extra on a parcel receiving, right?
Importers need to check with their customs authorties to find what personal amount is for postal imports.
3. What about if I want to sell my item through my website to a customer in the EU? Do I myself need to register in IOSS scheme and then deal with EU import VAT system?
Please see below link for information on IOSS.
VAT Import One Stop Shop Scheme
4. Asking the questions above, does something change if instead of an EU country it will be any other country? (America, Australia, Asia or anything else - rest of the world). And general question - I know that there is a threshold on £135 - is this a summary of all goods in one particular parcel in total? Or each item shouldn't cost more than £135? Thank you very much for the work you do and help that you provide.
£135 threshold is for personal imports into UK, each country will have its own regulation so please check with importing countries.