Does Uranus rule Aquarius?

In modern practice, yes. The classical table gives Aquarius to Saturn and has never been rewritten; modern astrology adds Uranus, and many practitioners read the sign through both — Saturn for the structure it builds, Uranus for its refusal to be governed by one thing for long. Both answers are current. A reading should be clear about which of them it is using.

Is Uranus a generational planet?

It spends about seven years in a sign, so everyone born across that stretch shares the placement. What is not shared is the house it occupies in an individual chart and what it makes contact with there, and that is where an actual reading happens.

Is Uranus a difficult planet to have?

It is disruptive by description rather than by temperament. Its contacts tend to end arrangements that had already stopped fitting, and whether that reads as damage or as relief usually depends on how much of the arrangement was load-bearing.

Planet

Uranus

Uranus is read as the part of a chart that will not stay inside an arrangement it has outgrown. Where it sits, things tend to hold steady for a long stretch and then change shape quickly, and the change is nearly always experienced as arriving from outside — whether or not it did.

It is one of the outer planets, slow enough that a whole cohort is born under the same placement. What makes a reading individual is never the sign on its own.

The planet that arrived

For as long as anyone had been casting charts, the scheme ran to seven bodies and stopped at Saturn, which is the furthest thing the eye can pick out. Uranus was found with a telescope in 1781. It was the first addition to a list that had been closed since antiquity, and the discipline had to decide what to do with a body nobody had ever accounted for.

What it decided is visible in the rulerships. The classical table gives Aquarius to Saturn and still does. Modern practice gives Aquarius to Uranus as well, and astrologers hold the two together in different proportions depending on the school they trained in — which is a live disagreement rather than a settled rule, and worth knowing about when two competent readings of the same chart do not agree.

That a body discovered by exceeding the limit of the eye came to stand for the break in a settled arrangement is a neat story, and neatness is a reason for suspicion. Take it as an observation instead: it is the reading nearly everyone in the modern lineage works from, and it survives contact with actual charts better than its origin deserves.

Questions

Does Uranus rule Aquarius?: In modern practice, yes. The classical table gives Aquarius to Saturn and has never been rewritten; modern astrology adds Uranus, and many practitioners read the sign through both — Saturn for the structure it builds, Uranus for its refusal to be governed by one thing for long. Both answers are current. A reading should be clear about which of them it is using.
Is Uranus a generational planet?: It spends about seven years in a sign, so everyone born across that stretch shares the placement. What is not shared is the house it occupies in an individual chart and what it makes contact with there, and that is where an actual reading happens.
Is Uranus a difficult planet to have?: It is disruptive by description rather than by temperament. Its contacts tend to end arrangements that had already stopped fitting, and whether that reads as damage or as relief usually depends on how much of the arrangement was load-bearing.

Two things that are easy to over-read

A body this far out spends roughly five months of every year apparently moving backwards, so a natal Uranus in retrograde motion is ordinary rather than significant. It is worth checking whether a reading that makes much of it has noticed how common it is.

And a planet named for interruption invites interruption to be found. Most charts are not in the middle of an upheaval at any given moment, and a Uranus that nothing else is pulling at is generally just sitting there, describing a capacity that has not been called on.