If my opponent controls a Wall of Shards with three age counters on it, how many times will Ajani's Pridemate trigger if she pays the cumulative upkeep?
In general, "For each ..., do this ..." happens simultaneously. (For Selvala, it's "For each nonland card revealed this way, ... you gain 1 life". For Wall of Shards, it's "... you may pay 'An opponent gains 1 life' for each age counter on it" [C.R. 702.23a].)
And in both cases, it's one source causing the life gain (C.R. 118.9), Selvala or Wall of Shards.
If my opponent controls a Wall of Shards with three age counters on it, how many times will Ajani's Pridemate trigger if she pays the cumulative upkeep?
Once. Cumulative upkeep's cost is paid all at once.
702.23a. Cumulative upkeep is a triggered ability that imposes an increasing cost on a permanent. "Cumulative upkeep [cost]" means "At the beginning of your upkeep, if this permanent is on the battlefield, put an age counter on this permanent. Then you may pay [cost] for each age counter on it. If you don't, sacrifice it." If [cost] has choices associated with it, each choice is made separately for each age counter, then either the entire set of costs is paid, or none of them is paid. Partial payments aren't allowed.
Private Mod Note
():
Rollback Post to RevisionRollBack
I'm a former judge (lapsed), who keeps up to date on rules and policy. Keep in mind that judges' answers aren't necessarily more valid than those of people who aren't judges; what matters is we can quote the rules to back up our answers. When in doubt, ask for such quotes.
If my opponent controls a Wall of Shards with three age counters on it, how many times will Ajani's Pridemate trigger if she pays the cumulative upkeep?
In general, "For each ..., do this ..." happens simultaneously. (For Selvala, it's "For each nonland card revealed this way, ... you gain 1 life". For Wall of Shards, it's "... you may pay 'An opponent gains 1 life' for each age counter on it" [C.R. 702.23a].)
And in both cases, it's one source causing the life gain (C.R. 118.9), Selvala or Wall of Shards.
Once. Cumulative upkeep's cost is paid all at once.