I'm a single solo founder. How much equity should I give to new cofounders / partners?

Why on earth do you need a CTO for that job description? If the product is done, funds aren't likely an issue and you don't need a team to pitch @ pitch competitions if you functional and presumably decent product. Sounds like you need a product guy which you could easily hire who could network with you and avoid title and paying s/he more as well as save your equity. Just a thought - no need to give away the house!

When bringing in a new cofounder it's important to give them an opportunity to earn their equity. Typically this means a vesting schedule over a certain period of time. For example you may decide on an opportunity to earn 10% of the company over 4 years with a 1 year cliff. This means there is no equity earned for the first year. After the first year they would immediately receive 2.5% (for the previous years work) and then a prorated amount (.2%) each month after until the end of the fourth year. This helps everyone's incentive stay aligned.

Now, in your situation it's important to understand why you want a CTO cofounder. From your description it sounds like you already have everything you need. Think about this first.

If you still want to find a tech cofounder then consider the following when making an offer:
What you would want if you were them?
What are they giving up to join you?
What will build a long term relationship?
What is the company worth without them?

The amount of equity can be supplemented by a salary, amount of time committed, or other compensation. Without knowing the specifics it's very challenging to give an exact % answer.

ZERO - there doesn't appear to be any benefit giving away your company.

Let someone BUY in if you really want someone on board.

Ultimately you can hire people extremely good and extremely affordable at what they do.

What you describe as required is an employee