I'm not sure I understand all the questions, but I'll give it a go.
1) Without lifting the Chef unlock, you can only cook on the cheapest grill or fire pit, both of which you can find in Buy mode or at a grilling area.
2) Yes, to everything
@HelenP wrote about grillable meals if you have all ingredients in inventory and the Bodybuilder restriction on only a single stack in personal inventory.
Regarding fish grilling, I have Outdoor Retreat and a founder with maxed cooking, so the household lived off of Fried Fish (cooking level 3) at the start.
Until you can prepare Fried Fish (actually, it's Grilled Fish), you can prepare other dishes but must move one fish into your household inventory every time you prepare a non-fish dish.
Example: You've caught one fish & moved it to your household inventory. You can now grill a non-fish dish. There's quite a few grilled dishes that only require L1 cooking.
Fried fish is the cheapest grilled dish, though.
You can access the fish in your household inventory after you've lifted the Bodybuilder restriction.
3) I did just as
@HelenP did.
4) Gourmet cooking can be leveled by: (1) starting with a founder who has both cooking skills maxed; (2) cooking on a stove or chef station (requires lifting Chef career); (3) importing a Gallery sim (requires lifting the Oracle career); or (4) lifting Writer-Author to order Gourmet Cooking Vols. 1, 2, and 3. I chose Method #1.
5) What HelenP said.
6) I agree with HelenP on all her points. As you quoted from Pinstar: "The cell phone may only be used to take or quit a job." The only exception would be if phonecalls were a required for a daily task, like HelenP wrote. Even after my sims were allowed to take vacation days from school (lifted Business/Management), the kids couldn't phone to request a vacation day because Esport Gamer was still locked.
Like HelenP, these are my personal interpretations based on Pinstar's rules. Good luck with your challenge!