billabob

You can still get the Deoxys form avatars from redeeming Deoxys promos. So a Deoxys (Speed) promo has a chance to give you Deoxys (Speed) avatar, redeeming Deoxys (Attack) has a chance to give you an Attack avatar etc.

The requirements aren't outdated, they're still correct.
 
Snorlax: "Reward for encountering and defeating Patrick in a clan battle"
This means you have to do clan battles from the https://www.pokemon-vortex.com/your-clan/ page until you're lucky enough to be matched with Patrick. I don't know the exact odds but it can take tens of thousands of clan battles to have this honour, personally I bought mine on Pokebay for 12 million.
 
For the other 3, there's only a chance of unlocking the avatar after catching/evolving those Pokemon, it's not guaranteed. That's why you don't have them. All 3 of those sell for ~1M on average so it's easier (but less fulfilling and fun) to just buy them on Pokebay

It depends on the time in real life, not in the game. Don't trust HyperPanther, you can just wait a couple of hours

There's no way to control how much you get, it's random. You can get 25K, 50K, 60K, 75K, 100K or 375K with each being rarer than the last. I've done about 700 immunes and only won 375k twice.