So, I don't really know if I still qualify as a newbie, but I'm hoping that that doesn't really matter... I don't know if these questions have already been asked, but I couldn't find them so I hope this doesn't inconvenience anyone who has seen this questions multiple times.
How does one access the sylestis other users put up for breeding/selling?

Via Advanced Search.

You just click "Search pets"
> can select species, theme, traits etc.
(If looking for purebred pets, > select species, > select either "Yes" or specific theme, > set "Include Purebreed" to "Yes" or "only" (depending))

But specifically for selling
> swap the "For Sale:" to "Yes", putting in specific price range optional
> Switch "Order By:" to "Sale Price" and "Ascending"

Same for breeding, but it's "For Breeding:" you need to set to "yes" and "Order By:" to "Breeding fee"

Thanks!

I literally do not know where the link that says "(Switch to Equipment) is in my inventory. Either i'm blind, or something's wrong with my account.

bellow the big 'your inventory' at thee top of the page there should be a smaller blue writing Switch to Equipment, click on it. ^-^