Is it possible that your friends can join your Hamachi server when they don't have Hamachi?

No.

Hamachi uses internal routing protocols. Basically, this means that all IP addresses are never exposed to the public web.

Inside your house, your IP address is 192.168.1.15. As you have obviously seen with trying to host a Minecraft server, your friends cannot connect to that IP address, because your friend isn't on your router. If your friend was at your house, he would be able to connect to that IP.

With this in mind, we can see what Hamachi does. It acts like a giant router. When you're connected to Hamachi, your computer gets another IP address, like 25.164.236.46. Any computer on your Hamachi network can access this address. Similar to above, this is like your friend being on your WiFi and playing on your server.

In short, Hamachi is basically like the WiFi router in your home, only anyone with your Hamachi network key (and the app) can access it.

However, there are workarounds and ways so your friends can connect without Hamachi. This is usually referred to as "Port Forwarding." There are many guides on how to set this up online. Be advised that your ISP may consider this to be a violation of their terms of service, which may result in your internet getting disconnected.

Nope. They need to have Hamachi installed. The IP addresses Hamachi uses are not accessible from the public Internet.