I recently learned the Trader profession and build a trading house. But I can only trade with one other city (I'm in Madrid and can only trade with Berlin).
Is it due to difficulty level, starting city - or am I doing something wrong?
I thought I'd perhaps get more routes when increasing my rank (both trader rank- and/or citizen rank) but so far no.
Anybody know?

I didn't try that occupation so far, so I have no idea how it goes, but the game probably lets you expand business considerably at trader level 3 and 5, as with other occupations.

Tried that already (as mentioned above), and didn't get any more routes when I upgraded the storage shed for next level.

Started a game in Berlin, and there I bought a storage hut and it had 3 trade routes.
Looks like it is either random (doubtful) or due to city.

Rafael: If I recall correctly all you get is added capacity to the sheds from upgrading the trader proffession...
Xandax, since you seem to have played the trader a bit do you know if the issue where clicking the trade routes would bring you back to the previous screen as in the old version or has this been fixed in the GOG.com gold version?

Now I started a new game, but I didn't find the occupation "trader". How come?

You can't start out as banker or trader but have to spend the 8AP on learning it during play.

I didn't get kicked back to the previous screen when clicking trade routes.
My (only) problem with trader is that it is confusing why you don't get trade routes despite being able to see the markers on the map.
Whether a bug, or how the game is - I can't figure out (yet).

A common issue with this game. Controls are sometimes unclear or unresponsive. There should be a easier way to understand or get into of certain situations.
Anyway, perhaps one thing you could do in this kind of situation is holding Ctrl, useful to see "clickable" areas of the screen...
So I can't start as a trader, but after achieving that profession, what kind of businesses can I run?

You can run the Storage shed line - which means you can send (horse) carts to foreign cities and trade some items there as well. Usually they buy between 3-6 different merchandise which change a bit and sell 1-3 you can pick up.
Usually prices are around what they go for in "your town", but at times they go up to trice the value (uhh nice :) and the stuff they sell can be down to trice lower.
It is a bit sporadic income, but potentially you can bring in a load of cash through that profession. One trip to a city netted me about 15K profit with a load of silver rings.
One thing to be aware off is that trade in other towns happen in their currency. You can exchange to and from these in the money houses.