The first rule I follow is pretty simple:
Get paid for what you do. Earn a return on what you own.
If you are running your company prudently, you should earn a salary for the position and responsibilities you hold within the business. This salary should be competitive. You should be able to replace yourself in the business at this salary. If your title is "President" or "CEO" - look for market rate salaries for others in that position within your industry and company size. If you wear multiple hats in a small business, you will likely have to blend this salary based on those various positions.
Based on how you run your business, the money left over at the end of the year after you and your team takes a competitive wage is your profit. If there isn't any profit, then you might want to do some work on your business model. But if their is a profit, then it's a clear return on what you own and not just a payment for work completed. The idea would be that you could exit the business as an operator, pay someone else to do exactly what you do, and you would continue to get that profit return at the end of the year. This is when a business acts like a true asset.
Whether you take your money in salary or profit distributions (or dividends) depending on your structure, taxes are about the same. W2'd salaries get normal employee contributed taxes, but then of course the company matches these. It is identical if you take a guaranteed payment or distribution that gets hit with self employment taxes. Profits are also going to get hit with the same taxes.
1) A fair salary would be a competitive market wage for the position you hold within the business. What is left over would be considered true profits and not just fabricated profits by taking a lower than market wage to boost the appearance of profitability.
2) Shareholders requesting salary information would be covered in your Operating Agreement or Shareholder Agreement. This might be terms you set with your investors. Or you might simply set a term that you only need approval if a single salary exceeds a cap (like $250,000). Which would mean you would need to present why you deserve a higher salary and have your board approve (if you are governed by said board via your investors). Profitability is a different ballpark. Your investors most likely have a right to see a monthly, quarterly, and/or annual Profit & Loss statement which should clearly state profitability. I can't imagine running a completely closed book company to my investors. Actually... I can't really imagine ever investing in a company where I am not permitted to see the financials.
Something to also consider here is the threat of trying to keep your profit numbers low in order to not pay taxes or to pay yourself a higher salary. If you ever plan to sell or exit the company, most widely accepted valuations of a business are done from profits (or EBIDTA). You might think you are saving yourself a couple points on taxes by avoiding profits in the short term, but if you exit the business and get a 3-5X (or even up to 12X in some cases) multiplier on your annual profits, you might be kicking yourself for trying to hide them through your accounting practices. Buyers will often sniff out an owner who created false profits by not paying themselves, but what's harder to do is figure out how much profits should have been when there were none on the books. By saving yourself $100,000 in taxes this year, could add up to close to $1,000,000 in an acquisition.