Here's the specific setup of triggers and resolutions in this instance:
You cast Lone Missionary
Lone Missionary resolves, entering the battlefield and causing 3 triggers to happen at once: one from Lone Missionary, one from Soul Warden, and one from Soul's Attendant. You choose the order they are put on the stack (we'll say Soul Warden, Soul's Attendant, Lone Missionary).
Lone Missionary's ability resolves: you gain 4 life; Ajani's Pridemate's trigger goes on the stack.
Ajani's Pridemate's trigger resolves: it gets a +1/+1 counter.
Soul's Attendant's ability resolves: you gain 1 life; Ajani's Pridemate's trigger goes on the stack.
Ajani's Pridemate's trigger resolves: it gets a second +1/+1 counter.
Soul Warden's ability resolves: you gain 1 life; Ajani's Pridemate's trigger goes on the stack.
Ajani's Pridemate's trigger resolves: it gets a third +1/+1 counter.
Unless your opponent wants to respond at a specific point, or you're playing in a serious tournament setting, the actual order of these abilities won't matter much. Your Pridemate will get 3 +1/+1 counters, and you will gain 6 life.
On to your second question with another example:
Say you had only a Pridemate and a Soul Warden on the field, then summoned another Pridemate. Soul Warden's ability gains you 1 life, and two requests for +1/+1 counters hit the stack, one from each Pridemate.
Before those triggers resolve, your opponent shoots the first Pridemate with a Lightning Bolt, sending it to the graveyard.
But wait! There are still two abilities sitting on the stack that say "When this ability resolves, put a +1/+1 counter on Ajani's Pridemate." So does your remaining Pridemate get both?
The answer, sadly, is no. Though the abilities appear the same, they are tied specifically to the Pridemate they originated from. The first ability will resolve and put a shiny +1/+1 counter on your brand-new Pridemate, but the second ability will search the battlefield in vain for the first Ajani's Pridemate before fizzling out.
Why is that? Because when a card refers to itself by name in its rules text, it means "this card only." It does not mean "any card with this name" or "all cards with this name." So you can't pick and choose where the +1/+1 counters for your Ajani's Pridemates go.