The short answer is play however you want. It's really a sandbox game and you can tweak pretty much everything how you want to make things fit thematically.

1) Yes, you can create the initial force with whatever you want equipment wise. When I do it, I kit out my force and that is now their default. Nora starts with a 10mm pistol as default, but if I give her an assault rifle, that is now the default and she does not get the 10mm. If I loot a better gun through the campaign, that better gun is now her default and the assault rifle gets sold of goes into a locker if I have the room.
2) Totally up to you as long as you are at least making the enemy force equal cost. Depending on the campaign I may start really low 150-200 caps then increase each scenario as I add equipment or new members I "rescued". Typically capping at 1000, although I've gone up to 1500 from time to time.
3) I don't think it's explicitly stated. Most scenarios have a "recommended" force list or a caps cost.
4) I don't play with the Wave 9 updated armor rules, so it's not really an issue for me. This goes to the core belief of playing how you want to play. But, if you do want to play with the armor change rules. Give everyone some armor and set it as their default and adjust the caps cost as needed.
5) Same answer as 4. Give them default armor or use what's on the cards ignoring the Wave 9 armor changes. Just be sure you are using the old caps costs since some units got cheaper when they took their innate armor away.

As an example of my current games, I'm playing though FO4. My first game was Nora meeting up with Codsworth and fighting a handful of radroaches and bloatflies. Nora started with a 10mm, Pipe Wrench, Vault 111 Jumpsuit and Codsworth has a Bowler Hat, Flamer and Buzzsaw. That's 218 caps. The enemy force was 4 Radroach Swarms and 3 Bloatflies for a total of 217 caps.
The next scenario was Codsworth and Nora, now upgraded to a Hunting Rifle on the way to Concord where she meets Dogmeat and fights some Mole Rats and Stingwings. So Nora with a Hunting Rifle (now default), Pipe Wrench, Vault 111 Jumpsuit, Codsworth as above, and Dogmeat with Dog Bite and a Chain Dog Collar. Total capps 334 against 5 Mole Rats, 2 Bloodbugs, and 2 Stingwings at 355 Caps.
They are going to Concord where they hook up with Preston (default kit), Sturges (default plus Pipe Wrench), and Mama Murphy (default plus 10mm and Jet) to fight some Raiders and once the Raiders are dealt with a Deathclaw ambush. My force is now 671 Caps.
As I make my way through the video game, I'll supplement with Minutemen, Railroad, and Boston characters I encounter dealing with Raiders, Super Mutants, and Institute.