Old time bike. Can I put a rear derailleur? Hi guys,
I am looking to build up an old timer bike and I have found this frame. Can I put a rear derailleur in that socket?
Yes, that is a standard derailleur hanger. Before attaching a derailleur, make sure that the hanger is aligned straight. There are tools to do this, but you can usually tell by eye if it's out of alignment. On a steel frame like that one, you can typically bend the hanger back into alignment with no problems. Also check that the threads are not stripped. If the threads are damaged, you may be able to use a thread tap to clean them up, or in the worst case, insert a helicoil. If you're not familiar with a helicoil, search "rear derailleur hanger helicoil" for examples. They will usually come with instructions for installation.

With regard to the dropouts, horizontal dropouts were standard on bicycles for many decades, whether they were single-speed or multi-geared. Look at pretty much any picture of a bike from before the late 80's. The only difference from a vertical dropout frame is that you have to pay a bit more attention to aligning the wheel properly in the frame when you put it on. Check that the wheel is properly positioned with respect to the brake pads and that the rim is equidistant from the chainstays. From your picture, though, it appears that the dropouts on this frame have stops in them, so that you can simply pull the wheel back against the stops. If they are set up correctly, the wheel should be aligned properly when seated against them.