[RPG] Do Eidolons need proficiency feats to benefit from armor

The approximate assumed wealth by level for a seventh level character is 23,500 gp, so you could afford such an item but it would account for half your wealth. Of course, specific campaigns vary, and if you have a party crafter you can halve the cost to you. And youe WBL about doubles every two levels so probably by level 9 it's more affordable, if it's a major part of your build.

No, eidolon levels do not stack in any way with animal companion levels.

An eidolon is not an animal companion so cannot benefit from Pack Flanking in any event.

However, I suspect you should probably be asking instead what your actual problem is - unless one or both of you have a lot of rogue levels, there's perhaps other better ways to reap a +2 to hit on your opponent, you have mentioned no real reason that you need flanking specifically. For flanking you could possibly use Gang Up instead, with another party member or, you know, a summon.

No, Snatch does not negate the need for the Grab evolution.

There are three components at play here.

1. The functional capability of automatically initiating a grapple on hit
2. The "grab" special attack, which grants that capability
3. The Grab evolution, which grants the grab special attack

So #3 gives you #2, and #2 gives you #1.

From the Snatch feat (emphasis mine):

The creature can start a grapple when it hits with a claw or bite attack, as though it had the grab ability.

So Snatch grants #1 from the list above, but not #2 or #3.

From the description of the Swallow Whole evolution (emphasis mine):

... The eidolon must possess the grab evolution, tied to a bite attack, to take this evolution. ...

So the Swallow Whole evolution requires #3 as prerequisite.

Snatch lets you grab without having the grab special attack. But the Swallow Whole evolution explicitly requires the Grab evolution, so you can't use Snatch to qualify for Swallow Whole.