It's not mandatory. But it's incredibly hard to get hired out of school, even a top one, if you don't do any internships. You gotta grind from day 1 in this world.
Depends on the country I guess.
In New Zealand it's mandatory for Software Engineering (and other engineering), but not for Computer Science, as it's a science degree.
Not at the vast majority of schools in the US.
Traditional universities have "summer vacation". :)