Is the WAN IP of an ADSL modem likely to remain the same if it is not rebooted?
Is an ISP likely to change the WAN IP while the modem is in session?
To specifically answer your first question:
The modem doesn't need to be rebooted by the user in order for the IP to change when the connection is assigned a dynamic IP. The ISP can initiate the change and you may notice a slight "blip" in your connection, but not necessarily a complete drop out and loss of connectivity.
To specifically answer your second question:
Assuming you have a dynamic IP, this would depend if the ISP has set intervals for changing the IP or if they wait for inactivity over a period of time.
To elaborate on the topic in general:
Whether your connection has a dynamic IP or static IP is something that is controlled by the ISP. Most modems (if not all modern modems) will display basic information about the WAN connection, including IP address, DNS servers, ADSL connection details, and whether the IP is dynamic or static. To find out whether you have a static or dynamic IP, I see that you can do one of three things:
In the event you have a dynamic IP, the frequency that it will change is determined by the ISP. I have been with an ISP that changed dynamic IPs once a month, and another ISP that changed much more frequently. I have also been with an ISP where the IP would change when I rebooted the modem.
If you need to RDP to a computer that is on a connection that has a dynamic IP, I would recommend using the services of http://www.dyndns.com. If you are not familiar with DynDNS, it is a free service that "allows you to point a hostname to a dynamic or static IP address or URL".
For example, instead of keeping record of what the dynamic IP is, you can use DynDNS to map a hostname (such as cjohnstone.dyndns.com) to the dynamic IP and simply RDP to the hostname from that point on. And should the dynamic IP change at some point, a small piece of software is used to update DynDNS at regular intervals so the correct IP is always mapped to your chosen hostname.
Not without dropping the connection, but if you disconnect and re-connect it may change.
I've been with a number of ISPs over the years and most don't seem to change even over a period of months (I used to have a domain name pointed at my IP and it tended to stay the same for a long time).
Admittedly, my experience is with cable modems, not DSL. But as far as I know the modem doesn't have a bloody thing to do with the IP address associated with the computer or router connected to a larger IP network via the modem.
The IP address is (typically) assigned using DHCP, a protocol which functions at a level higher than the modem. The IP address assigned by DHCP usually has a limited lifetime. When the client's lease expires it is supposed to renew the lease. At that time the DHCP server would technically be allowed to negotiate a different IP address. So, yes, it could change.
In practice it rarely does. But you should not rely on this. After all, isn't that why dynamic DNS exists?
It depends on your ISP on the frequency of WAN IP change for your connection - but yes, always assume that ISP can and will change your IP.
For example, I am on an ADSL ISP currently that renews my WAN IP address at least once every two days, and you should be able to access your modem logs to see how frequent are the changes.
The best thing for you to do if you want a run a personal FTP, or RDC server, or WWW server, is to use a Dynamic DNS service. This is a service where they give you a human readable address, such as myrdc.dyndns.org, and then even if you have a dynamic IP, this address will be updated to point to the new IP everytime it changes.
Alternatively, inquire with your ISP on Static IP plans, where you are assigned an IP and it never changes. It costs more though.