What are they actually doing in America to stop Trump?

It's a bit like whack-a-mole. You bash down one bad idea of Trump's, and another pops up.
It is great that the citizens are climbing above the deliberate shock tactics, and are beginning to gain some 'wins'.

The only thing that matters to most Americans is money and fame. The media made Trump by putting him on their screens and people thought he must therefore be very special because he had so much money.
They also loved him because he wasn't a politician, and for some reason they gave him the most political poweron the planet.
Many continue to love him- many are worried but feel afraid to say so because that's how facism works. Others hate him and want him gone and they are growing in number...

Are we learning the lessons from the US experience? From the media and the supposed popularity of reform I would say not and may well find ourselves in a similar situation very soon...

Wasn't there talk of impeachment ?

Here are some links about legal challenges. A bit of Googling will find more. there are also many social media pages reporting on organisations resisting in states such as Oregon, Minnesota, and many more.

www.youtube.com/watch?v=4ZVv0ClUjSQ Oregon's top legal battles, court cases against Trump administration through 2025

www.youtube.com/watch?v=CnXKWSIf26M a federal judge moved swiftly to block an effort to freeze $10 billion in social safety net funding

www.youtube.com/watch?v=_71mgSkivD4 Supreme Court rejects Trump's bid to deploy National Guard in Illinois

nevadacurrent.com/2026/01/14/ford-highlights-legal-battles-against-illegal-unconstitutional-entirely-immoral-trump-actions/

www.lawdork.com/p/on-year-two-of-trump-two

www.nytimes.com/interactive/2025/us/trump-administration-lawsuits.html

www.justsecurity.org/107087/tracker-litigation-legal-challenges-trump-administration/

www.lawfaremedia.org/projects-series/trials-of-the-trump-administration/tracking-trump-administration-litigation

I’m assuming, and don’t actually know, it’s because the Republicans pretty much dominate both Congress and the House of Representatives (have I got this right?)

So Democrats have little authority or power?

In my view I’m astounded no one is appearing to do much to stop him, but I have read of some of his actions being halted by the courts.

Also, I don’t really understand the “executive orders” process, but on the surface these seem to allow the POTUS to do more of less what they choose.