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The main thing to understand is that formally, those 2 options are not active at the same time, you get first the option to discard 2 cards for +$2, afterwards (if you chose to use the previous option or not) the option to pay $2 for +2 Cards.

The game wants to minimize your clicking, so

a) if you have 2 cards in hand and $2 once the options start, you are given both buttons. That way, if you want to only use the "pay $2 for +2 Cards" option, you don't have to explicitely decline to use the first option, you just click on the second button and the game interprets that as "don't use the first option".

If you want to use the "Discard 2 for +$2" option, then click on the button, and you will be given the option to use the "pay $2 for +2 Cards" option afterwards.

b) If you lack either $2 (and also have no Coffers) or 2 cards in hand, the corresponding option will not be initially given. This is the situation in your first picture (no $2). If you lack the $2 but have the cards, after discarding you usually have the $2, so "pay $2 for +2 Cards" option will be given afterwards (but you didn't discard in your game).

c) The game generally does not go from one phase to another "during the middle of an effect". In your second picture, if you discard 2 for +$2, you have $2, could pay it for +2 Cards, and continue with playing Actions if you drew Action cards. But if you don't want to discard, your Action phase will end, as you can no longer do anything in it (no Action cards in hand).

That's why the "Don't" button appears in that case. The game could show the "End Actions" button, but for some reason does not do that and uses this "Don't" button for you to indicate "No, I don't want to use any of the given options, please end Capital City now".

[don't click "Login"]

This looks to be the "Spinning Castle" problem:

You need to open a private(Firefox) or incognito (Chrome) window , go to dominion.games, enter your Name and Password, but don't click "Login". Instead, click on "Kick and Resign" (rightmost of 3 buttons below the login data area). Then you should be able to login normally (no need for private/incognito tab).
Modify message

Contract is not an Action card, it is the first (natural) Treasure - Duration card. That means it's not eligible to be played with Scepter.

It has the golden Border that indicates that there is/are some card(s) associated with it. For Contract, that means you put an Action card aside to be played next turn. It works similar for cards like Gear or Archive, that have cards set aside for their own purpose.

Yes, logging the pile makes sense. I'll forward this.

Done!

Thanks for the report! That is indeed a bug, which I've forwarded.

I'm not sure what happened in this case, generally the feature seems to work, I just tested it. Unfortunately from other reports it seems that sometimes the server that is responsible to get you the right  data between games is sometimes not correctly doing that, so errors like that happen.

There was a general problem with login at around the time the last messages where posted. If it still persists, can you post screenshots of what you see where it doesn't proceed.

I'll forward that as suggestion.

You can set your min card pool level to 2 to get the same effect as waiting for expansions:



You can even put it higher, to make sure even more cards are in the pool from where the kingdom is selected.

OTOH, since subscriptions run on level 1 (free, no subscription), 5 (core subscription) and 10 (complete subscription), the next level after 2 to make a difference is likely 6. In theory players who use lots of promo codes may have ean effective card level somewhere in between, but those are IMO rare.

Yes, that was a longstanding error, because initial german printings had similar (and even the same) names for both cards, so the online version used different ones. But since at least 2019 the German names are not changing any more in printing, it seems.

For the previews, those are over now, so you don't see the option any more.

For the games with your friends, the question is why those need to be rated. If you want to play kingdoms that lean a certain way (like the "theme kingdoms" you mentioed), then you can certainly do that with unrated games.

What does the Tables screen of your friends look like when they open it? For me it looks like this



You can see several games with more than 2 players, including Ingix2 (4 slots, 2 yet unfilled) and also from "Hart Attack", "Haufan" and more.

Make sure your friends have all the marked buttons set to the "lighted" state, as shown above. They are especially there to make it possible to see only tables with a certain number of games.

Done!

The developer checked for the "Dominator01" account, and all seems OK (1 year left for the subscription).

What makes you think that you are "basic" right now? If you start a bot game, will it have non-base cards? If yes, can you post a screenshot of your automatch settings?