Learn German: Das U-Boot sinkt. - The submarine is sinking.

Probably not, because it is redundant. The verb sinken already implies moving downward. However, you can absolutely use an r-word with a more neutral verb of motion, such as Das U-Boot geht runter (The submarine is going down).

What does the U in U-Boot stand for?

It stands for Untersee, making the full word Unterseeboot (literally: under-sea-boat). German capitalizes the letter in the abbreviation, and it is almost always shortened to U-Boot.

Could I use ertrinkt instead of sinkt here?

No, ertrinken specifically means to drown. It is only used for living things that are dying in water. For inanimate objects like a submarine, or for the pure physical movement of going underwater, you must use sinken.

English uses 'is sinking', but German just uses sinkt. Is there a way to emphasize that it is happening right now?

German does not have a present continuous tense (an 'is doing' form). The simple present sinkt covers both 'sinks' and 'is sinking'. If you really need to emphasize that it is happening at this exact moment, you would add an adverb like gerade, as in Das U-Boot sinkt gerade.