AFAIK
Yes, there is heavy dictatorship in Uzbekistan (second heavy dictatorship in xUSSR after Turkmenistan). It is quite possible to be persecuted there for being too religious Muslim (even far from terrorism) or gay. Uzbekistan is very populated and very poor.
Uzbek authorities chosen Tamerlane as a main national hero.
Uzbeks have reputation of very conservative, patient and hard working people. There is comparably low immigration from Uzbekistan (in proportion to population). Uzbekistan is rather closed country.
There are many ethnic Uzbeks in surrounding countries and they often are victims of local nationalism (namely in Kyrgyzstan). Uzbek refugees from ethnic conflict are not welcome in Uzbekistan and there is no effective support policy from Uzbekistan of Uzbek diaspora.
Yes, there are some gypsies everywhere and they are most mobile.
If a refugee can be accepted in Sweden he will definitely prefer it to Russia for better life conditions. And if a political refugee are provided with better treatment than any immigrant will prefer to be a political refugee. Even for the price of being gay.