This spell is just like other spells that have come before it - flame blade, mage's sword, spiritual weapon... Spells that have been around since forever, so this isn't really new, and we can easily divine rulings based on those precedents. In fact, flame blade is just about exactly the same in nature (different school, but whatever).

• Proficiency rules don't apply since it's a spell not really a whip, as ruled by Joshua Frost on the Paizo forums for flame blade and scimitar proficiency. It also can't be sundered or disarmed, you can't hold anything else in that hand...
• It doesn't "also" do weapon damage, they just do the damage listed. No reference, that's just how we all know all those spells work.
• All those spells behave like weapons in terms of other feats, effects, etc. - see this entry in the Paizo FAQ. Weapon Focus, Arcane Strike, bard song, etc.
• As it's conjuration(summoning), yes, augment summoning would work just as it does on a normal swarm. The effect is a "whip like swarm." Its benefits are modest but functional. Since it can turn into a swarm it would be weird to have different DCs in one form than the other.

It's a spell that summons a swarm that then acts like a weapon. I know that's somewhat confusing but in the end, it's pretty cool, so use your best judgement.

The rules are ambiguous, but I think they lean to "yes."

As you know, it's not explicitly spelled out in the DMG. But I think they lean your way, and here's why:

1. On p.128 "Crafting a Magic Item" lays out the prerequisites for a character to craft a magic item: (a) a formula for the construction; (b) a spellcaster with spell slots--Magic Initiates need not apply--and knowledge of any required spell; (c) character level minimum.
2. Later, near the end of that section, we find a few paragraphs dealing with ancillary matters: lifestyle while crafting, custom items, and assistance. The paragraph on assistance calls out the character-level prerequisite for any assistants, but doesn't mention the other two. The designers could easily have said "if each of them meets the requirements to create the item," but instead mentions only requirement (c) from above. Admittedly, an argument from omission is pretty thin.

Unfortunately, there's a decent counter-argument of nearly the same strength: "anyone who assists is a co-creater, and thereby must meet all the creator's requirements. The level requirement is simply called out to make it clear that another spellcaster with the right spell but not of the right level could not assist." Of course, this line of reasoning would moot "if each of them meets the level prerequisite," which I find intolerable.

But it doesn't matter, because it's explicitly your call. (Of course, all things are ultimately your call, but this one's called out as such in the DMG.)

Back it up to the very beginning of "Crafting a Magic Item":

As an option, you can allow player characters to craft magic items. (loc. cit., emphasis mine)

Obviously we all understand the "golden rule" of GM-ery: Make decisions and adjudications that enhance the fun of the adventure when possible. (Repeated at the start of all of Wizards' published adventures, and a good paraphrasing of "The Dungeon Master" from the introduction to the DMG.)

But I'd suggest a broader understanding of published materials: what we purchase in the core set is not (just) a game. It's a system, with a game as a worked example included. The rules presented provide you with a default game playable out of the box, but also everything you need to construct a game after that fashion. Every rule, in my opinion, is preceded by a silent "and here's one way to do ___:"