when using A dynamic DNS website can you host any IP address you want?
Yes, you can. If using DYNDNS, or No-IP, you need to install the updater on the computers which is port forwarded or any computer in the network to auto-update.
tHEN if you host that to your router the next time you are assigned a new IP address it will be the one you hosted?
Yes. The updater will scan for new IPs every 5 seconds, which will auto-change it to the new IP.
Also how long would the hosted IP last for until it changes?
It depends on your ISP. Some change very often, others change maybe once a year.
i would like to keep the same IP address all the time
You are referring to the "static" IP. Most ISPs nowadays give static IPs, but some still give dynamics, so sadly, until your ISP changes its methods, you will have to live with that problem.