Anyone who thinks Russia hasn't mixed politics and sports is pretty much ignoring history.
No, they shouldn't be allowed to. Players shouldn't be kicked off their club teams, but I don't see the issue with restricting the national team. The idea is to punish Russia and national teams are symbols of Russia.
I also am iffy, thinking about it, on banning Russian club teams. The only banned team is Spartak Moscow, though, and its owners are oligarchs in Russia's oil industry and may face sanctions. And there are other issues in terms of sending RBL into a country on the precipice of martial law.
For what it's worth, in other situations, I would be okay with Russian athletes competing but not under the Russian flag. But when it comes to national teams, it's different. Perhaps unfair, but at the end of the day, I'm not really interested in the argument that Russian athletes are the real victims here, especially when we've seen Ukrainian athletes who have been killed trying to protect their country.
As for bolded, yes, completely. I think the West should open its borders to any Russian national who wants to leave Russia.