Can I replace this with that fork? (see pics)
 

Can I replace this:

http://i120.photobucket.com/albums/o.../old_fork1.jpg

with that:

http://i120.photobucket.com/albums/o.../new_fork1.jpg

?

The new fork fits nicely in the front tube and the bearings only seem a bit more exposed, but looking at the new fork detail, I wonder if the bearings would be seated correctly?

And if the new fork wouldn't work, what do I need to buy to make it?

The bottom fork doesn't have a bearing race on it (that black thing that supports or "hides" the bearings on your other fork). I recommend having a local bike shop remove it from the top fork and put it on the bottom one. I used to do it myself, but it was a crude method along the lines of using a plumber's wrench to remove a bottom bracket.

There are several issues in play here:

1. You need to get a new crown race for the headset you will be using. The old crown race you show is clearly indexed (i.e. it's junk) and should be discarded. New crown races can be purchased separately. Get one that properly matches your headset. Any good LBS should be able to do this for you. Take the fork and the frame to the shop for them to see. You need the head tube I.D. and the crown race seat O.D. measurements (accurate to 0.1mm) to match components.

2. Is the 2nd fork ("that") chrome plated? If it is, and you need to get that crown race seat reamed, then you might have a problem. All cutting tools come with the warning not to use them on chrome plate. You'd have a hard time getting someone to ruin a very expensive cutting tool on that. This is a reason that chromed forks should always be avoided, unless there is some compelling reason to get one. Keep your fingers crossed that a new crown race will seat without a problem. The good news is that they usually do.

3. Given the condition of that old crown race, it's probably best to invest in a new headset. You can get a decent Tange-Levin threaded headset for a fork like that for about twenty dollars. Do yourself an additional favor and chuck the caged bearings and replace them with loose balls. With occasional service, these headsets will last a long time.

Thanks guys, I took very seriously into consideration both your suggestions. I hope I can get away without buying a headset.

Re. chrome fork: yes, that's right, it is chrome-plated. I like it, it would have given the touch I was looking for, to my fixed gear bike. I am aware that chrome plated surfaces are hard to machine (chrome is the hardest non-compound metal), but I didn't expect it to. Well, let's see if I'm in the **** or not. After the holidays I'll visit my LBS.