For what would they hold the administration in contempt and what does this do to block, stop, or reverse illegal actions?

It seems like you're lacking a basic understanding of how law and government work and it doesn't seem like you know what contempt means. And, to make up for that, you throw out witless insults in an attempt to derail the conversation.

You, "the internet", are far too emotional to consider the reality of these situations. Just because something makes you angry or someone does something you think should be illegal does not mean someone is not permitted to do that action.

There are absolutely actions that Trump has done that are illegal and many of those actions have been decided on while other cases are in court now. "The Democrats", I presume we're addressing Congress, are not explicitly the group responsible for holding the administration accountable for everything he does. Congress only has authority over a handful of things (mostly, but not limited to, money) with few options to do anything about them.

The point I am trying to make is; (1) what actions does OP suggest are illegal, (2) a court has to determined that action to be illegal, (3) Congress is not responsible for suing the president nor responsible for determining what is legal nor responsibly for jailing an executive officer, (4) this Republican Congress is not going to pass legislation (the main power they have) to block, stop, or reverse actions taken by this administration. And, finally, what the Trump administration is doing, legal or not, is largely what the United States voters voted for. So, the best way to stop these quote unquote illegal actions is to vote for Democrats in two years.