Yes. It does affect the longest road: the road stops at the settlement for counting purposes, and starts again at the other side. Yes. Both players who possess roads into an intersection have the option of building the third road out, regardless of whether a settlement is there or whose it is.
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Can you disrupt a settlement?
If you build a settlement on his road, you disrupt it yes.
Is it legal to move a road?
Yes it is a legal move you can find an example on page 11 of the Almanac. Essentially as long as a road has a connection to a city it can be broken up.