Russian citizens can stay in Belarus without registration for 90 days from the date of entry. If you plan to stay longer, you need to obtain a temporary or permanent residence permit.
You can fly from Yekaterinburg to Minsk by direct flight (tickets are available from 21 thousand rubles) or with a transfer (from 9 thousand).
Visa-free entry to Armenia with a Russian passport is valid for up to 90 days. You can enter with an internal document only through airports, at land borders you will need a foreign passport.