A big question is what would happen if your corporation could not meet payments? Can you declare bankruptcy in Eve? :)

No you can't.

Most of the time roles are basically sorted to the following arche types.

Auditor - Can you view this information?
Personnel Manager - Can you shift people around, give roles, take roles, fire/hire?
Supplier - Can you move items from this container to the other container?
Financer - Can you give corporate isk away? can you spend on behalf of the corporation? can shift funds from one wallet division to the other?
Logistics - Can you move space assets, change passwords on them, anchor bases in the name of the corp?

What players do within these archetypes or how they mix them up or the overall goal of the corporation overall is up to the players. Some are seriously running the business of whatever 'even if that business is empire building/maintaining' some just throw caution to the wind and let the stuff fly.

No you can't.

I've given some more thought to two facets of skills mentioned.

Facilities Management (Decrease cost of all property holdings by 5% per level)
|----> District Management (Decrease owned properties maintenance and purchase cost by 4% per level; increase output of garage and clone production facilities by 4%)
|-----> Planetary Management (Strengthens Network Security and Facility Output by 20% on one designated district; additional skill levels expand number of fortified districts; maximum 5 fortified districts)

Network Management
----|------------->Network Security (4% Complexity to District Drone Run-Time AI; Increase Combatant Hack Subroutines by 5%; )
----|------------->District Sensors (Increase Incursion Beacon Sensitivity by 3%;Increase Ground Sabotage Detection Bubbles by 2%)
----|------------->Communication Subscriptions (10% lower clone communication package price)

In order to make developed corporate skill sets rare they should require tremendous skill investment on the latter end of the skill tree. For example:

Facilities Management (2x Skill) 621,840 sp at Lvl 5
District Management (6x) 1,865,520 sp at Lvl 5
Planetary Management (12x) 3,731,040 sp at Lvl 5

/ / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / /
Total investment 6,218,400 sp
/ / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / /

The entry point is low and geared toward development toward core operational abilities. As one moves up, their corporate skill should almost reflect a tactical weaponization of offensive and defensive capabilities, albeit not with a gun but a person's prowess to enhance the gears of war.

The purpose of acquiring this data dossier is to aid in setting up contacts for backdoor deals with members of rival corporations to splinter infrastructure by switching allegiances thereby taking vital skills away from the corp.

The operations of these skills would be passive meaning one does not necessarily have to log into Dust for their skill attributes to count towards corporate operations. In turn this could also mean that lone wolf players have an ability to use their two additional alt characters as dummy silent partners in the delegation of some parts of corporate skills.

Corporations pay for various logistical and operational costs with recurring weekly payments. Such things may include transportation, network communication subscriptions, ammo use, and weapon licensing. However, the cost of these thing may be offset by investing into skills within the corporations tab. Attributes such as efficiency management and distribution networking would offer price cuts over time that would assist you in keeping your corporation solvent. Without proper skill investment, these costs would make it very difficult to maintain a lone wolf corporation and purchase the necessary equipment to remain competitive on the battlefield.

Absolutely not. This is a terrible idea. There is nothing wrong with creating a single person corporation in Dust or Eve either for personal preference or specifically as a tax-dodge, and there is absolutely no reason to impose arbitrary maintenance costs for any corporation (or to require skills to reduce such costs). What you're proposing has no precedent in Eve and all, precisely because it arbitrarily disincentives certain behaviors that players should be free to pursue. For active corporations with lots of programs and activities (vehicle reimbursement, corp battles, or in Eve, corporation hangar space, ship replacement, joint market ventures, corp logistics services), then there will already be plenty of overhead costs. Adding overhead costs just because "we need overhead costs" is harmful. If you want to run a shell corporation for you and your friends, or just yourself, there should be absolutely no strings attached.

What you're proposing has no precedent in Eve and all, precisely because it arbitrarily disincentives certain behaviors that players should be free to pursue. For active corporations with lots of programs and activities (vehicle reimbursement, corp battles, or in Eve, corporation hangar space, ship replacement, joint market ventures, corp logistics services), then there will already be plenty of overhead costs.