Deep technical adjudication is exactly what judges in higher courts are equipped to do. No matter the domain, they are presented with tortuous technical language and jargon about a specialized topic (the statute), a collection of nuanced facts, and two or more carefully organized logical arguments, prepared by the parties' capable lawyers, about why those facts activate or don't activate this or that clause of the statute.
Probably a lot? Judges are perfectly capable of learning technical topics and are pretty smart in general. The judge who presided over Google vs Oracle taught himself to program. Some may be old but don't forget the people who invented the internet are 70s+ right now.
That's a good question. Tech issues are tough, which is why you see lots of friend of the court briefs to explain it.
For FCC matters around net neutrality, there's generally two courts: the DC Circuit Court of Appeals and then the Supreme Court.
And, yes, they deal with it and have clerks to help.
For instance, in the biggest decision about net neutrality, the BrandX case, where the FCC was allowed to determine that Cable companies were Title I information services, DNS is mentioned 13 times in the majority decision.
And if you find that interesting, I recommend reading the Scalia dissent, where he said that it's totally clear that broadband is a Title II service, and letting the FCC say otherwise was wickedly wrong.