Yes and yes.

As you have practically embedded every relevant rule, I will only give the reasoning without citing the sources.
Spiked Chain Training makes it double weapon, double weapon means 2 one-handed weapons, one in each hand, and you can attach those. Embedding only works with some specific weapons, and the spiked chain is not one of those. It is not hidden, as only embedded components can be hidden.
Imagine it as a scarf, extending from one hand to the other over your neck.

Houseruling it so that it is embedded and hidden would not be overpowered however in my opinion, so talk to your DM.

Do not forget to add Dual Implement Spellcaster to your Eldrich Stike, as you make an arcane attack while wielding an implement in each hand.

There is one catch however, you have to enchant the item yourself, as a Pact Blade has to be a light blade, and Spiked Chain Training does not make Spiked Chain a light blade. You can enchant it, as you treat it as a light blade.

No

All weapons have weapon category (pg.279) such as simple, martial, or advanced. Weapons also have other traits, such as agile. The Rogue sneak attack feature (pg.181) requires the use of either:

• A melee weapon with the agile or finesse trait
• An unarmed attack with agile or finesse trait
• A ranged weapon

As you said, the Ruffian racket also allows you to sneak attack with any simple weapon.

A weapon you utilize through the Unconventional Weaponry feat can only be used with sneak attack if it fits into one of those categories. Unconventional doesn't change the weapon category, it only changes how you calculate your proficiency.

So no - it's not true that any weapon accessed through unconventional weaponry qualifies for sneak attack, because it's not automatically a simple weapon. However, if you choose an uncommon simple weapon (such as a clan dagger or katar) you can use it for sneak attacking.