Per-day abilities need to not weaken you for the rest of the day, which is the same concern for both magic and psionics because neither has any inherent penalties for use and buffs can last quite a while;
Depends on availability. If high, like D&D(you literally cannot finish using them across the standard 4 encounter day), then having a penalty(one that lasts across multiple encounters) induces the player to avoid blowing them in the early encounters...or encourages the 1 round work day if nova is still possible.
Lots of ways to manage this.
Per-day abilities create the 15-minute work day, which is the same whether you're dumping four encounters' worth of prepared spells on one encounter or four encounters' worth of power points on one encounter;
Indeed. There is some leeway where resources are concerned, though D&D tends to focus on the daily effects.
Encounter resources are instanced, which makes them good for combat balance because their availability is consistent, and their refresh cannot be hurried, but terrible for dramatic tension because you don't weaken.
Hourly(or similar gradated regeneration methods where you recover X amount of Y resource every interval), gives a middle ground, they work for pacing and tension because it's
just fast enough that waiting it out feels cheap(a psyche tactic mainly) but the party would tend to preserve some in reserve so they can take the next encounter with their usual ease if it turns up early. It can also mean that fully nova-ing puts you at
below a day's worth of recovery, which gives you deep reserves to push through a boss encounter or campaign, while discouraging reckless expenditure because it's too much trouble to sit it out.
Campaign resources take extended time, peace
and often specific locations to get back in more than trickles. It's a pretty quick way to ensure people are miserly with their resources. Not always suited to the group, since a lot of players can't manage things on this timescale well. It does preserve peak capability while lowering median capability though.
Per-day abilities are too binary, which is always the case in D&D given its save and AC paradigm; both spells and powers can be either too powerful or worthless, and the marginal utility of being able to spend juuust enough PP for a certain effect (assuming you can figure out exactly how much you need to use) is basically the same as lower-level spells auto-scaling by CL.
More or less a D&D-ism, nothing to do with the resource model. A bunch of spells generate absolute or unresisted effects, others don't. So some effects last until an immunity consistently comes into play which obsoletes them. While other stuff would go in a bell curve(unavailable->potent but limited->impotent and unlimited), absolute effects is basically a plateau, once it becomes available, it'd always be relevant.
There are a lot more, but pretty much all the factors are rooted in D&D 'traditions' and resource models. What psionics give over vancian is more granular access to power, and more things cost appropriate to their effects(due to augments, you'd generally be spending the right amount of resource proportion to challenge ratio) Vancian is also much, much bigger resource pool than psionics, allowing effectively endless stamina.