Is there a Gemini search engine?

I've found this one:

gemini://geminispace.info/

Needs a client to access, of course. Basic, but functional. I found a general-purpose forum not too different from reddit or lemmy through it (and they decided to call it a BBS, because the Eternal September hasn't happened to Gemini yet):

gemini://bbs.geminispace.org/

Is there support for Forms/server side code

To the best of my understanding (and it's highly limited, since I only just learned about this, so take everything with a grain of salt), what Gemini does is primarily limit what the client can do. No local scripts, highly limited markdown. The server side is not limited. You can write any complex code you want that works behind the scenes - but it still has to deliver static pages (called "capsules") to the end user. This series of articles explains the basic underlying tech and uses the example of a simple server to illustrate how Gemini works:

https://medium.com/erus-encodia/creating-your-own-gemini-server-part-1-what-is-the-gemini-protocol-cf497477c4d

And yes, forms are possible, even though there appears to be a somewhat widespread misconception that they are impossible. Please excuse the sketchy-looking IP address instead of a URL, this was the best resource I was able to find on this (and yes, I checked if this page is on Gemini - this appears to be not the case):

http://216.218.220.144/tutorials/sig-tutorials/misc/gemini-forms.gmi

Screenshot if you don't want to click on the above link: https://i.imgur.com/s2mL3bM.png

Disclaimer: This is two years old and I have not tried to implement it myself. Looks entirely plausible though.

How big is it? Is there like just a few sites or a few hundred?

According to the search engine linked above, there are 2420 domains and 1,854,666 individual pages as of yesterday. This is about comparable to the World Wide Web at the same time 1994, a number that grew to 10,000 by the end of that year; I wouldn't expect the same explosive growth from Gemini - the field has already been plowed, after all. Gemini Space is small, but not a ghost town.