Do I need an separate EFI partition for each OS sharing a common disk?

ESPs are usually shared across OSes, so no, you don't need a second one; but it also should not cause problems. That said, some tools or OSes may become confused by the presence of two ESPs. The Windows installer is the only example of which I'm aware. (This affects Windows 7, but I don't know about later versions.) If you run into such a problem, you can always change the type code on the ESP you don't want the Windows installer to use -- even just temporarily. (A temporary change can be useful if you want to install two Windows versions, each with its own ESP.)

The location of the ESPs relative to your other partitions makes deleting either one awkward -- to recover the space, you'd need to move the start point of at least one partition, which is time-consuming and dangerous. This may not be worthwhile to recover only about 200 MB of space -- but then again, your disk is only 120 GB. You'll have to judge just how precious your space is, vs. the time and risk involved.