Probably not. US Patents are the cheapest patents to get.

If, say, a German company infringed on a US Patent by selling to a customer in France, that would be completely legal, unless the US Patentholder also had a French patent, which is often not the case. They'd have to prosecute in French court as well, which, given the size of France's market vs. the US, would be Pyrrhic (with a capital P) at best.

The calculus for being a patent troll requires a bizarre confluence of factors (size of market, expense of litigation, certainty of litigation, cost of patents, venue procedures) that are likely to limit the phenomenon to the US.

Other countries also have a loser-pays-costs rule for lawsuits, so the risk to NPEs are much higher if they lose an expensive case.

And also software patents are non-existent in the EU as far as I know so it would not work at all.

IANAL, but no (if I understand correctly). Companies outside the US (all the way outside, with no US footprint) are subject to the laws of their own land. You could sue them in US court, and never collect a dime. You could sue them in their own courts, have the lawsuits be subject to the laws of their land, have to spend a lot more money on lawyers... and still (probably) never collect a dime.

If they have an office in the US, though, you can sue the US division in US court.

If they have no office but some sales in the US, I'm a little less clear on...

Only if the company outside of the US trades in the US. But that normally involves setting up a subsidiary, in which case they do have a US company.

There is no such thing as an international patent.

There have been a number of cases of the terrorists going against US-based customers of non-US entities.