Which Ip address type changes: external, internal or both???

I can certainly understand your confusion, but it's actually not to difficult. Your external address can change and most ISP will have this arrangement. This will mean that you will need to tell your friends your new external ip or utilise DDNS (Dynamic Domain Name service if memory serves me correctly). This is quite simple. You register with a provider such as dyndns , (there are others but dyndns is at the top of my head), and you get an address like myserver.dyndns.org you can share this with your friends etc and they can access it. When your external ip changes dyndns gets notified of the new address and users can still use myserver.dyndns.org this is usually setup in your router settings under something like dynamic dns.
An alternative is to request a static IP address from your ISP this will mean your external IP won't change usually this involves an addtional fee if your ISP offers it. So that is external IP which is the IP that the world uses to interact with you. Lets take moment to help clarify the roles of external and internal IP addresses. You are browsing the web you click on a link. That request is passed from your computer with say ip 192.168.0.2 and that heads to your router at 192.168.0.1 which also has ip say 212.255.212.254 (completely random so might not be legit but it is an external ip for the explanation). The router forwards the request on toward its destination. The server replies and it makes its way back to 212.255.212.254 (your router) the router looks to see which Internal IP to send it to and sends it on its way to 192.168.0.2.The 192.168.0.0 etc adresses are internal IP addresses and help the computers in your home to find each other. The 192.168.0.0-192.168.0.255 (might be different range but still reserved) are reserved for home network use and you will commonly see people with these ip addresses. These are internal and can't be used on the internet because my 192.168.0.1 is say my router but it could be the same in your home or anyone elses home. So thats why an external address is used, also because we would run out of IP addresses if each device had its on IPv4 address. Your router/gateway is given an external IP and it has an internal IP that way it can communicate with all of the computers in your home and an external IP to communicate with the internet essentially acting as like a bridge. Fyi this is called NAT (Network Address Translation) just a fancy name for take my external IP and share it with all of my home computers. Don't worry too much about this unless you want to learn more.

Internal IP addresses are either Static or Dynamic (changing)
Static means you must go to each device on the network and manually input its network ip subnet mask and gateway. Not too hard with say less than 15 devices these IPs will not change unless you change it on the device. DHCP (? Dynamic Host Control Protocol) is very common. This is usually setup on your router, (make sure only one device is acting as a DHCP server) so you turn on your computer it needs an ip it sends a request the router receives it responds suggesting an ip a some other stuff happens and long story short it gets an ip from the router. There is a 'pool' of available addresses. An address from this pool is assigned to the computer for say 24hours and if it isnt renewed ie its disconnected from the network the address returns to the pool. This way addresses can change since its a take what you get sort of deal which is great if you don't need something like port forwarding. This is where DHCP Address Reservation comes in. An IP can be taken out of the pool so that it is not given away to another device. When say your server comes on it requests an IP and the router sees the server knows that it should give it the reserved address and attempts to do so. The router needs MAC addresses for it to know what device your server is. This is usually done with a range for example the first 10 IPs on my network are reserved for servers printers etc and from there on is where all the laptops phones and non essential pcs get their ip's. DHCP Reservation is kinda the best of both worlds.

Man I ramble too much hopefully this hasnt confused you. Post back if you have any queries