After a resolver resolves a DNS name to its IP address, for example, www.google.com to its numeric IP address, is this IP address a classfull or a classless address?
If its a classless address, how does the router knows its subnet mask?
Classful routing has been replaced with classless routing (CIDR) more than 20 years ago. Everything is classless.
Routers on the path don't need to know the subnet the destination host is on. They just follow aggregates routes. Only the last hop router needs to know the subnet, which it will know because it's part of that subnet. If a physical subnet is even used, because there are plenty of other ways to handle traffic (load balancers, VXLAN etc).
In short: All routing is classless, and you don't need to know the subnet mask.