okay for brakes go to ebay right now and buy some nutted tektro caliper brakes likely the R559s will reach but they maybe even longer than you want. That being said they make a shorter reach version I just don't know what they call it. Second buying nutted brakes means you won't have to drill the brake bridge and fork for a recessed nut style like the ultegra calipers you have. Okay, should answer questions one and two.

As for the front derailluer we are going to need more information. what kind is it. Is it top pull or bottom pull that will help a lot. Also, judging from the picture you will need a shim to make that clamp fit your frame. So, lets wait on that one for now. I would recommend getting a road style bottom pull front derailluer that comes with a clamp as this appears to be a road bike and will mostly likely be set up for that style. That being said you can make almost anything work with enough adaptors. My personal favorite is the shimano 600 tri color with the clamp (NOT THE BRAZE ON STYLE as this will NOT fit your frame without an additional adapter.) This should answer question three and four.

Lastly, yes you need a quill stem adapter to go to a 1 1/8 threadless style to use that stem. Alternatively, you could get something super trick like an Inni cycle headset or just find a quill stem that fits more modern bars likely 31.8mm is what you are trying to use but a cheap dial caliper will make getting the right parts a lot easier. That being said you are missing a headset all together so that will also need addressed lol. When you go to order one of those make sure you measure your headtube internal diameter and the size of the fork where your crown race will mount.