I do have a problem with foreign companies( or foreign subsidiaries) owning US patents, copyright trademark etc. if it's a US patent, trademark copyright you should pay a US tax on earnings from that.
On the flipside, imagine US companies licensing necessary patents (such as those for colored shapes or round buttons) from foreign companies that are made extremely expensive because the licensing is heavily taxed and full of fees by foreign governments.
Presumably they do: a US patent only protects you if you are selling something in the US. Assuming that sale shows up somewhere as someone's profit, there would be an income tax from that.