When you need Energy more than you need catnip. Pasture is much safer to upgrade, due to demand reduction inherently having pretty strict diminishing returns. Demolishing your aqueducts capriciously can very quickly put you in a starvation situation. If you're not sure whether it's safe, you can sell them off one by one and see what happens to your catnip production. In early runs, energy production is relatively unimportant, and you might be better off not bothering at all. In later runs, you might never build the catnip-producing buildings in the first place outside of Challenges like Winter Has Come or Atheism that remove the hefty production bonuses you build up over many runs.
Hydro plants also cost a fair amount of titanium, so you may want to wait until you have good titanium production before switching.
Data centers do the same thing as libraries, but better, and then some, so there's not much to worry about. If you want to be ''sure'' you don't lose any max science, one data center provides the same max science as three libraries, though this isn't accounting for the compendium cap increase. Be aware that astronomical events will cease to occur if you have 0 of both buildings, so definitely don't upgrade if you lack the requisite 10 concrete and 100 steel to build the first DC.
Switching to Data Centers will decrease your bonus for crafting blueprints (since you'll have fewer data centers than libraries). And Data centers consume 2 watts of energy each.
For Happiness purposes, a single broadcast tower can replace your entire stock of amphitheaters. For culture purposes, a single tower increases the cap by as much as six amphitheaters, and increases production as much as ''two hundred''. There's very little reason to ever delay this upgrade, unless you simply don't have the metal to build a tower.