What's this mean: "Owner"

Shareholder-Employee...

"does not want any personal payment/reimbursement - prefers to retain the service income in the company."

What's that mean? They get paid through Payroll, right?

"These are my questions: What are the entries to record the owner's expense (loaded time) that will not be reimbursed to the owner?"

The "Owner" is an employee and is an Expense to the corporation because of payroll. The Labor is income if they charge it to a customer.

"What are the entries to record the overhead and fee?"

Again, that would come from Sales. You are asking about Gross Sales, or Costs? Payroll is the Cost. There is no such thing as "fully loaded."

"Will the above 2 entries allow me to generate invoice through Accounts Receivable and capture revenue too?"

What you haven't done is identify this activity. A Discussion, such as:

Either a person contributed their time outside of the business, or they contributed as part of their business.

An S Corp has no provision on taxes for Contribution.

A business can Waive Sales Price. That doesn't make it a contribution. That makes it a 100% discounted sale. Sales Taxes might still apply.

We can't help you generate an invoice, because we don't know the program in use.

You didn't identify if the work was done for a Charity. Like this discussion:

I am a consultant. I get hired for a project for a 501(c)(3). I invoice them In Full. I also give them a credit memo showing I wrote it off. Now they have proof of Professional Support from the community. Meanwhile, I have forfeited a sale.