How do I block someone from offering me trades?

No idea but to be fair one could have said the same thing about the trading section on here going back years... until the recent update of course.

Mm, IDK but it works as well as always. There was some drama about the domain renewal that turned out to be paranoia.

Yep, there are several discussions like this one from June:

http://steamcommunity.com/groups/bartervg/discussions/0/351660338684119228/

Speculation is that barter.vg could fall apart any time now (domain was mysteriously renewed earlier this month, until then people were worried that it would stop working somewhere before the end of the month), but it's a very valid platform, so hurry up if you want some quick trades :)

Abandoned, no. 237 days ago, Barter, who'd been chatting with people daily up till that point, vanished entirely off the internet. He hasn't, for example, logged onto Steam at all since then. Abandoned indicates intent, whereas here.. it's far more likely something tragic happened.

As long as the site is still running, it's still usable- it was designed to be mostly self-sufficient. Add in that SteamTrades feedback is still being used for barter trades in addition to barter feedback, and it works exactly the same as making a ST trade, except you've got the benefit of the far superior barter interface to arrange the trades with in the first place.

In other words, as concerned as some of us are about the circumstances around the creator, the site itself is still working just lovely, and is still highly recommendable.