Those commands are actually independent of each other, as they use two different private keys. This means there is a possibility that 2faok gives proper tokens, but 2faok can't fetch the page, neither accept any confirmation on your behalf.

If you've ensured that you're not doing anything wrong, that is, you're using the command against the bot you truly want to confirm as (usually your main, so 2faok <YourMainBotName>), you did wait at least half a minute since making a listing (since Steam sometimes takes some time before confirmations pops up) and the issue doesn't resolve itself within a day or so, you're most likely using invalidated key for confirmations, which means that you need to remove ASF 2FA and link it again - ensuring that the secrets you're importing actually work fine before you do so.

Of course you can also take a look in the logs, perhaps there is something meaningful there. Regardless, bottom line is, you need a valid private key for your account, if the issue is not a temporary Steam network failure, you're out of luck, since it works for me right now, which means Valve didn't break the ASF's code from working.

Completed set after matching should trigger inventory notification which will automatically trigger send completed sets if you configured it properly - after matching is over.

Because that's send trade period, it sends everything, not completed sets. Also, completed sets does not mean "finished games", but set possible to craft, which is also probably not what you mean.

And do you have ASF 2FA to confirm the trade ASF is going to send?

You have the URL of failing request, ensure the machine with ASF can reach it as expected.

If your machine can't reach the gtm.you1.cn, then ASF can't either. This could be also temporary Steam issue, then as ASF says, just try again later.

ASF does not work with hours played at all, apart from recording them off the badges page for cards farming process, and exclusively because we need that info to make optimal decisions - your game does not display there so not a source of information.

It might be possible to grab this information from Steam directly, but for that you'd need to code custom ASF plugin that would hook into the communication and actually record it on its own. A lot of work for something this small. I don't have any more ideas.

Any action on Steam can result in permanent blocking of accounts, since as written in https://gtm.you1.cn/storesteam/subscriber_agreement

Valve may restrict or cancel your Account or any particular Subscription(s) at any time

Nobody here can answer whether or not your actions will or will not cause temporary or permanent bans.

2faok command can confirm Steam family invite confirmations without any issues, you only need to wait a bit before the confirmation arrives since the moment you get notification to do so, as Steam sends that confirmation with some delay - half a minute should be okay.

2FA section on the wiki for more details on how to enable ASF 2FA. Commands I assume you already know, but if needed, commands section is there for you as well

1. Yes.
2. No, maybe with third-party plugins.

The only way to find out is to wait for the sale and see what happens.

It's too early at this stage to say whether it'll work or not. It was rather exception that it kept working for all these years without bigger edits.