As funny as it sounds, Shark Tank or Dragons Den is not an awful show to watch to think about the kinds of Q's that you may want to ask. There's a lot of drama that is made for TV and the process of giving an offer and acceptance on the spot is not how that actually works, but they do ask good Q's to try to understand the company, the customers, the growth potential, etc.
This was exactly my first thought. Some companies are on there just for publicity / drama, but if you look at the serious discussions, they do have good questions.
I did loan money once to a bakery that was moving out of a home kitchen / farmer's market stand into a retail space. He had a small business loan coming, but the bank was dragging its heels and his first month's rent was due. I had been his customer and gotten to know him for over a year. It was a small amount of money, and he named 10% as the interest. I didn't haggle--Would have done it as a favor, but he has his dignity, and the business was growing up.
Back to your situation: agree with the questions given. Trust is one thing: you don't want to be suckered into a scam. But they will most likely be out of business in 5 years, despite their best efforts. It's a dangerous world out there!
Questions:
What has your revenue and profitability been each year since startup? What are your projections for this year and beyond?
Are you working this full time? What are you paying yourself? (If you are investing, they *should* be paying themselves something; otherwise, their profitability is inflated)
What is the equity for this investment? (and therefore, company valuation) What will the investment be used for? What further investments will be needed down the road?
What are your distribution channels? Which are the most profitable? Which are growing? What ones do you want, that you don't have?
How are you marketing?
Who are your best competitors, and what are they doing that makes you think so?
The best answers would be ones they know immediately, to show they have been thinking about it. The more specific the numbers are, the better. Notes are fine-organization means a lot too. But blowing off your questions, or obviously improvising an answer is a big danger sign. I also like Mark Cuban's red flag of quoting big total market sizes rather than focusing on your specific opportunity.