> 1. How much does religion play a role in homophobia in Russia?
Religion has relatively a little role in Russia at all. In the last years government tries to seriously increase influence of religion in society, but "70 years of communism" still has it's effect: russian society is relatively low in religion. Institute of visiting churches is very rare for example. Even they who believe themselves to be believers in most cases are just "it's convenient to believe there is no death after death" + carma + reincarnation and no visiting church.
It's hard to talk about "role of religion" about almost anything.
> 2. Why was being gay a crime in Russia?
Tzar's criminalization of gays was canceled after october revolution (and even serves as example for other countries), but was returned in 1934. Wiki says that it was initiative of NKVD. They believe that "hidden nature of homosexual clubs attracts anti-revolutionary elements". Stalin approved. Despite of these facts there is no doubt that gays were perceived as "bad thing" in that times, so probably it was just a matter of time. After USSR fall gay criminalization was cancelled in 1993.
3. Why do you believe Russians to be homophobic?
Russia lags behind Europe in this matter by 20-30 years and that is all about it. Shifts in perception of homosexuality from 1990 till now are tectonic. However, this process is not completed of course.
4. What rights to LGBTQ person have in Russia?
AFAIK, they are free of conscription to army.
5. Why do you believe violence against LGBTQ persons are tolerated?
See (3). Violence is not tolerated, if it's crime then it's crime. You may have biased view on Russia.
6. Are you familiar with the Russian anti-gay propaganda laws in Russia?
Yes. It's convenient move for government. Restriction on "propaganda among minors" allows to block parades, because streets are full of minors, but at the same time freely allows to gay clubs to exists. Tacit approval of majority of electorate is applied. You may compare it with british
Section 28.
7. Do you have an opinion whether or not LGBTQ rights have evolved in Russia?
Yes (see 3)