Do I need upgraded rings for the achievement

It is to cut load times when traveling to Firelink Shrine. Since all of the services (leveling up, merchant, blacksmith) are inside of the shrine, the player has to travel back every time they want to do something. Instead of loading the entire area, the game only loads the much smaller interior of the shrine. The fogwalls are there because the outside of the shrine is still loading, and will drop as soon as it's done.

Yeah, aside from the appearance, nothing really changes.

All rumors about losing souls if we die with a hollowing level of 99 (which is the max) are FALSE!

I just tried, having a hollowing level of 99, letting myself be killed, and I got all my souls back after retrieving the bloodstain.

So, no downsides apart from the appearance, which can be solved by buying an Untrue Dark Ring from Yuria at the Firelink Shrine after Yoel dies, which allows you to keep a human form even though you're hollow.

And if you want to heal completely, there are several tutorials on Google. But it requires you to pay for as many levels as you gained multiplied by the amount required to level up at your current level.