There's so much good advice on that here. Steamdb.info is super handy too.

I checked out your stream out of interest. I don't have a Twitch account but you asked what the Puzzles section was. I'm going to assume that was in reference to what I said. Basically, the links and codes for giveaways are hidden behind certain puzzles and you may need to use different methods for solving. Like there's ones hidden behind jigsaws, nonograms, encryption, or just really smart techniques related to steamgifts website itself, and a bunch more that smarter people than I figure out.

The events come in with all these cool themes related to the giveaways. Some large scale notable events in recent times are from escollo (11th factory day), Conti (The Seventeen Days of Conti), gus (March is not a month, it's a MEGAEVENT), and Ottah (Welcome to Germany!).

I'm on my phone right now, so it's a bit hard to give links for each one, but if you go into the Puzzles/Events section and just type a keyword from each title it'll show up. They all ended but you can still work through the puzzles to get an idea.