Is there a legally mandated filing fee and/or deposit in the last instance?

The Lawof Ukraine on Court Fee (as of 2013, in Ukrainian)

Source: http://apladm.hr.court.gov.ua/sud9107/tax/

Article 4. 1. Court fee is charged at the respectiverate calculated from the minimum monthly wage established as of January 1 ofthe calendar year in which the appeal was submitted to the court, in a ratio tothe price of a suit and a fixed amount.

2. Courtfee rates are set at the following rates:

1. Forsubmitting to a court:

2) of anon-property claim 0.1minimum wages

8)appealing the decision of a court to the appellate instance, joining anothercase to an appellate complaint to the court: