Should I bother with this lathe?
Edit: I got the picture of just the lathe to upload finally.

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Frankly, this lathe looks rather wobbly. The headstock of a lathe should be very sturdy because there will be a lot of force on it. Take a look at this homebuilt (from wood!) wood lathe:
http://www.isobevel.com/woodlathe.htm
On your lathe I would want to fasten the two parts of the headstock together to minimize vibration. Welding may not be a good idea, though, because of the distortion produced.
I think I'd abandon that lathe and build my own, similar to the one in the link above. The chisels and other tools you have would be fine for almost any lathe.
Good luck!
You will need to de-rust it. There are several ways including electroplating methods described in Instructables if you search.
It may need some new bearings as well. Only you can tell if there is any play.
The tools will be OK with a clean and sharpen.
Most old equipment works well once operating. Worth a try.
They don't take up any room save them for future needs.
A
https://picasaweb.google.com/110570767727885011270/Lathe?authuser=0&authkey=Gv1sRgCN3oiLjBi5HZrwE&feat=directlink
I also do not see speed reducing pulleys or a chuck to hold the wood.