Mike,
In the order asked_
1) No difficult to do, but I would say having an additional oil feed to the rear cylinder was not that common a modification. The rear cylinder naturally received oil slung from the crankcase well, and seemed to get sufficient oil without additional means.
2) Yes. You can see pics of what the exhaust valve lift bits look like
in-situ further down in this post-
https://www.douglasmotorcycles.net/index.php?topic=2811.0and discussion in this post-
https://www.douglasmotorcycles.net/index.php?topic=2784.0and here-
3) ...but I think there is something missing that would have mounted on the portion of gearbox that is missing.
Not sure what you mean by missing part. The gearbox mount did evolve over time. For instance the type shown in your photo gallery mounts on a flat platform in the frame. For the 1927 season this was altered and the transmission mounted directly on extensions of the engine bearer tubes. So you may have a mix of early and late transmissions and frame.
4) Yes. And No. The kickstarts are fragile and Douglas did make them more robust over time. Yours is indicative of what normally happens with folk jumping on the kick starter and mashing the first few teeth of engagement. One of the cover studs acts as the limit stop, and repeated slamming into this elongates the hole for the stud and cracks the casting. The bend stud does make it awkward to get the cover off too! Douglas intentionally fitted the lever in a near horizontal position when at rest. Folk would reposition the lever higher, to get more swing. They would then be more apt to hit the stop following through with a hearty kick before the lever was all the way down to the ground. You can just dress the teeth up and live with what you have, or find a gear blank of the correct size and cut down into a new quadrant and weld it to your existing shaft.
Additional posts about the EW oiling system (because that is going to be your next question!) can be found here-
https://www.douglasmotorcycles.net/index.php?topic=974.0and here-
https://www.douglasmotorcycles.net/index.php?topic=1002.0Also in your picture gallery are some images of a plate retaining the tappet guides. These also evolved over time. The type you have thread in, and are prone to work loose as you can see. Later they were tapered and held in with a bridge clamp, similar in idea to the homemade version fitted to your engine.
-Doug
[update https links. 02Feb20 -Doug]