Will my minecraft server ip work?

I did not completely understand the first part of your question but i guess i'm gonna say the same i say to most. Port forward the default minecraft port (25565) and people can use your IP to join. I think you have to give them your public ip though so they can connect (try ipchicken to find out your public IP). Now as for the second part. By "words" i assume you mean something like this mc.example.com. To do this i think you need to link your IP to a domain of yours. These things don't usually come for free but i can recall finding a free one. Do your research and you are gonna be good. Both your questions can be found on google so i assume you didn't search first.

Yes a Valid IPv4 "Internet Routable" Number is Permitted. It must be your WAN IP Address. And not your LAN.
Don't Forget about the Port Number to also give out as well.

Example: http://99.98.97.96:33489

And Doesn't have to be a FQDN of www.example.com

FQDN is good only for Commercials sites where you want to be Found…
If your running a Server for Private use, you only need to give out its IP Address and Port Number.

**If you want your Clients can edit there own host file to associate their own name with your Server.

Host File Example:

99.98.97.96… Koolest-se…

If you have a static IP on your modem/Internet provider, you can purchase a domain name from Godaddy for about 10-15 bux a year, and point it to your external IP address. So in theory, you could own www.carltonsminecraft.com and your friendscould use that to connect. But to do so, you MUST have a static IP address (usually costs extra from the isp) and then setup port forwarding to allow the connections through the modem/router.

Assuming you have a router, you should do the following:

1) Set the server computer on a fixed (static) address on your internal private network.

2) Set up port forwarding in the router for all the ports used by minecraft so that incoming connections go to the server computer.

At this stage you should be able to access the minecraft server from the Internet using your public IP address as reported by

http://www.whatismyip.com

If your ISP assigns a dynamic (changeable) IP address for your public address, then this can change from time to time. To overcome this you can either check for changes using the URL above, or you can sign up to a Dynamic DNS service (DDNS) such as noip.com or dyn.com. This can provide you with a fixed URL (what you mistakenly called an IP with words) that tracks changes in your public IP address.

From what you have written in your question, when you say your server is on address xxx.xxx.x.x, I suspect this might be something like 192.168.x.y where x could be any number between 0 and 255 and y could any number between 1 and 254. If the address start 192.168. Then it can never be used on the Internet. This is one of the ranges of addresses that are reserved for use only on private networks. The same addresses can be used on different private networks without interfering with each other as they can't pass across the Internet. So to answer your question "Will this ip work for people who are not in the same network?", if the addresses start 192.168… Then they will not work if the network is being accessed over the Internet. It could work for two different networks in the same building providing the connection between them does not need to go outside (using the Internet).

You may give it a try, and do get LEO Privacy Guard v 3.0., It offers you various security functions, so as to keep your device absolutely secure.