Yes, there are two types of load-following: "bump up the power", or "lower it". This also applies do renewables: not producing (many wind turbines are equipped with a braking system) or wasting an excess of power isn't as challenging as quickly producing more power, then less, then more... fine-tuning and for extended periods of time.

Yes, running at full-tilt 24/7 is way easier for a nuclear reactor than doing the load-following game (on every account: total cost, maintenance, risk...). They are built for it!

Hydro: yes, to an extent because load-following hydro is mainly done by pumped-storage, many dams are of the "run-of-the-river" type and cannot always load-follow: if there is no incoming (upstream) water they cannot produce any power.