I generally capture with my VGA capture card directly from the real hardware and not from Dosbox, so can't help with the settings within dosbox, but I think there are some general topics I can speak about:

Great Hierophant wrote:

1. How can I losslessly convert the video, which uses ZMBV codec, into something friendly to streaming video? Is there a freeware program that will work?

Can't answer this question unfortunately, as I use Sony Vegas to do that job for me with the excellent built-in MPEG2 and H264 codecs. I know VirtualDub can do conversion very good, but it's not exactly user friendly.

Great Hierophant wrote:

2. For 16:10 videos, how can I add black bars on the top and bottom to keep the aspect ratio? My concern is that any video conversion to convert 320x200 into a 4:3 ratio, like 640x480, will introduce artifacts of some sort. Playback on a CRT with an adjustable vertical size control should allow someone to properly stretch out the video.

If the stretching is done properly, nobody will notice. A 320x200 image is stretched vertically on a 4:3 monitor to match 1.33 ratio, so to present the game properly, you have to do the same. Then again I'm unsure if Dosbox already does this for you when capturing.This video (showing that the Gamebroadcaster can capture unsupported resolutions) shows me using stretch function in Sony Vegas from the original capture resolution to represent a 4:3 image.

Great Hierophant wrote:

3. 70 FPS is very unfriendly to streaming video services. Is there a way to force DOSBox to redraw the screen at 60 or 30 FPS (with a VESA utility)? I would prefer DOSBox to do it instead of an external program, which will undoubtedly introduce loss into the video quality.

70 FPS I have no experience with, but atleast aim for 60FPS when capturing. Don't you think Youtube will be offering 60FPS in their videos very soon? I capture and render all my videos in 60 FPS. I'm very sure Youtube and other streaming services will support it very soon, just like they did with widescreen, 1080p, 3D, subtitles, etc etc. Also Youtube do a good job on the 60 to 30 FPS conversion, it's not something people will notice unless they know what to look for.

1. How can I losslessly convert the video, which uses ZMBV codec, into something friendly to streaming video? Is there a freeware program that will work?

2. For 16:10 videos, how can I add black bars on the top and bottom to keep the aspect ratio? My concern is that any video conversion to convert 320x200 into a 4:3 ratio, like 640x480, will introduce artifacts of some sort. Playback on a CRT with an adjustable vertical size control should allow someone to properly stretch out the video.

I don't think there's a way to get anything loseless that's remotely streaming-friendly, but I assume you simply want to minimize loss along the way. For conversion (and aspect correction) I can personally recommend FFmpeg.

Here's a useful article about using FFmpeg with captured DOSBox footage. Note the final example at the very end, which nicely tackles the ratio issue.
An additional tip: it's a good idea to upscale your video by a large multiplier, using blocky integer scaling (nearest neighbor interpolation). For a youtube source, if your video is 320x200, try a factor of 4 (1280x800) and declare a 4:3 display ratio as the article suggests: this minimizes any blurry ugliness when viewing the result.

You could, of course, play around with the choice of codecs. DOSBox outputs ZMBV in 24-bit color - FFmpeg reads this just fine, but unfortunately, it only writes ZMBV in 8-bit color, which tends to mess it up. So I wasn't able to get a completely lossless upscaled video out of it... but if you use a lossy codec with a high enough bitrate and q-factor, the difference won't matter much when it gets processed for streaming.

About the FPS problem - got me there... don't know if there's any good way around it, to be honest.

To do Retro Swim, I use Handbrake to get MP4s, which I can then use in FCPX.

Handbrake is great for the task, it lets you tweak nearly all the options for transcoding. I'm pretty sure it uses FFmpeg in the background, but it's a nicer GUI than FFmpeg's own, I think.

Handbrake is on Windows and Mac, possibly Linux too.