As Jim G said, a router typically forwards lookups to the IP of the DNS server it is configured for - To add... The benefit of this is that devices can register themselves in DNS so you can access via hostname - this would not work if you only used your ISP's DNS (excluding Netbios/similar).
As for the netmask... networking 101 time!
a netmask literally masks everything before it... For example,
255.255.255.0 can be:
XXX.XXX.XXX.YYY
In the same way as:
255.255.0.0 can be:
xxx.xxx.YYY.YYY
What I mean by this is, the subnet just defines what is on your own network, anything that isn't, requires you to go through the router. By using the range 192.168.1.x on a /24 (255.255.255.0) subnet, simply means that anything from 192.168.1.1-192.168.1.254 is on YOUR network, anything else has to go through the gateway.
By changing the subnet to a /16 or 255.255.0.0 simply means that your network is 192.168.0.0 - 192.168.254.254, but, as these are all private addresses, it really shouldn't make that much difference in a home network.
As to why it suddenly changed, and the fact you are using a bridge, all I can think is that it was either an update to the router/similar that caused problems, or a driver update on your machine.... but, it is an odd one.
The 192.168.* range is private so you can technically do this without causing IP address collision problems on the wider Internet. However, conventionally the 192 octet range is used for Class C networks, which have a subnet mask of 255.255.255.0, allowing communication across only one octet range of computers (255). What you are describing is a Class B network, which by convention uses 172.16.x.x
Convention aside, there is nothing stopping you from using the 192.168 range as a class B. If you wanted to limit network traffic to only the 192.168.100.x and 192.168.110.x networks, you could change the subnet mask to something that includes only that range, such as 255.255.240.0 (which would allow communication between any subnet in the range 192.168.96.1 - 191.168.111.254) - if you put the two subnets together (192.168.100.x and 192.168.101.x) you could change the subnet mask to 255.255.254.0.
A fun Subnet calculator to play with can be found at http://www.subnet-calculator.com/
Best Answer
Basically a valid subnetmask, when written in binary, has to consist of only consecutive 1's and then 0's, but no intermittent mixing. I.e.:
Edit: The first bits (the nonzero bits) could also be set to match the network address, the important thing is that if you perform a logical AND operation on an IP with the subnet mask you get the network address.