If I have an iPod touch (1st gen) can I install apps?
You can update an ipod touch 1G up to ios 3.1.3.  Finding available apps that work on ios 3.1.3 or earlier can be painstakingly hard using the Apple app store.  An app store app called "VintApps" makes this super easy.

https://www.facebook.com/VintApps313