With Dynamic Host Configuration Protocol (DHCP), IP addresses are "leased"
to the clients. These "leases" are for a set period of time and have to be
renewed at the end of the time period. The protocol provides mechanisms for
obtaining & renewing the leases.
On some routers you can configure the "lease period". You can go in and
change it - say - from 2 days to 2 weeks. On other routers it's
preconfigured & unchangeable. In a typical household network - with 2 or 3
computers - a long lease period works fine. But in an office network with
many users coming & going they will typically have a much shorter lease
period - so they can recover & recycle abandoned IP addresses.
Typically, the DHCP server will just go ahead and extend the lease for a
client requesting a renewal - i.e. the IP address does not change. This is
a function of however of how much contention there is for IP addresses.
If you have a client PC that you don't use very often - e.g. once every 3 or
4 days - and the lease period is 2 days, you may find that it winds up with
a different IP address every once in a while.
If you have Windows 95/98/ME you can view the lease time by running a
program called WINIPCFG. It will tell you when the lease was obtained and
how much time is left. If you have Windows 2000/XP, you can view this
information in a DOS window. Type "IPCONFIG /ALL".
To answer your other questions:
With regard to changing the starting IP address - NO, the router will not go
"OUT" and reconfigure the network. It doesn't work that way at all. DHCP
is a passive mechanism that's initiated by the clients & RESPONDED to by the
server. It does not reach out with tentacles & manipulate its clients...
If you assign static IP addresses to your clients, this does take effect
immediately, but you *may* have to reboot after making this change. If you
DO assign static IP addresses, you must assign them from OUTSIDE your
dynamic address pool. Typically you'll have a set of addresses available
like 192.168.x.1 through 192.168.x.254. Check your documentation / go into
the router config to find out which of these are in the pool. If you assign
a static address that's in the DHCP pool, you'll run the risk of getting an
IP address conflict (two machines fighting over the same address).