I like these questions a lot. Nicely done.
The set I use is below, with explanations. Note that this is entirely a b2b list. I don't think there is a meaningful list one can ask for consumer startups, since in my view the consumer space is purely the domain of the ycombinator "throw it at the wall and then double down on what sitcks" - there is no engineering, marketing, etc. that you can apply to a b2c startup that isn't working and I don't think you can ask anything other than "how fast are you growing?" for consumer stuff.
For everything else, though ...
1. What is the critical problem on the customer side? How intense is the problem?
The company should be able to explain one or two very crisp, very clear customer-side issues. This goes beyond "what problem are you solving" because solving problems aren't enough to get a buyer to take action. Diffuse or "nice to have" problems means you never have a champion or buyer who will simply say "take my money" and most likely the reason for the diffuse/dull/etc. issues are behavioral or structural and that no one will actually pay to solve them.
I cannot emphasize enough that PLANS TO ADDRESS STRUCTURAL ISSUES AT CUSTOMERS ARE ACTUALLY THE LINES IN A STARTUP SUICIDE NOTE.
The other thing you see a lot is that people try and shore up crap businesses by throwing a lot of things in the solution to address a lot of problems at once with the idea that the sum is more valuable than its parts - that is a body shop mentality, not a good startup position. Startups should have something that they address that people want to buy, not be the business equivalent of a "52-in-1" Atari cartridge. A collection of dull, diffuse issues means the solution will usually not have buyer priority. Worse is purely hypothetical """problem""" where product is just a vitamin or insurance = no buyer outside of compliance, which is super low margin and low urgency (lots of security plays have this, or worse, fail to recognize it). Let garbage vendor-integrators like IBM or Cisco weakly assemble an array of crap, low-margin products into a "solution", that is not a good startup business.
2. What is the solution? What does the solution directly and completely solve in terms of the critical problem? Why now? Is the solution a necessary part of other changes or is it in and of itself sufficient to have day one+ value without big changes on the customer side?
Another issue you see a lot is that the solution only works if the customers make other changes that would also partially alleviate the problem, and so the solution is actually part of a collection of important customer-side changes that are going to be impossible to get done in a repeatable way. The solution has to deliver value without large changes on the part of the customer, especially changes that would have helped alleviate pain _already_ since there's an obvious issue there that the solution startup is missing. Customer-side-changes also means sales repeatability will be very poor which is a death sentence for startups.
5. What is the customer type? Who is the buyer? What existing budget are you redirecting if any?
This is another issue that shows up a lot: businesses are broken into groups of functions with independent owners. If the startup's business spans multiple business areas and multiple business owners are going to need to cooperate (not just agree, but they have different timing, different priorities, and so on) that is a big problem.
If buying the solution has to come from multuple discrete budget line items, that is a big problem because that implies trying to coordinate what is effectively a sale to each of them, with different trade-offs and different priorities and timeframes, and then conclude the real sale after all of that. This is a serious momentum and timing problem because it's hard enough to rendevous with need-and-now customer side without having multiple gates.
If _both_ are required, that's a death sentence.
3. What is the value of solving the problem?
... And the actual cash on the table value of solving the problem is critical. Even if you have a very real problem, and even if that problem has acute frustration/pain/etc. on the customer side, it doesn't matter to a startup. There are, unfortunately, lots of real problems, even critical ones, that customers view (and can perhaps justify with a pure $ argument) as not being high value. No value = no margin. You need to be reducing CAPEX, OPEX, increase efficiency, increase user experience (and be very, very careful of this one because a lot of people kid themselves), etc.
6. What megatrends are in favor of this solution?
Also known as, "how much education are you going to have to do?"
Also, you have to ask yourself, "are mega trends independently solving the problem in a different way? are megatrends sucking the oxygen out of the room in terms of buyer attention?" Lots of businesses have "transformation" plans dictated by executives that intend to solve (or not) some business problem for purposes of their brand, and most of the time these are actually just trends at the CIO level, and they may not even be aligned with real pain points. These can sink you if the trend is against you.
7. Who is the team? Why is this team the right one? Why are they the ones to deliver a technical solution?
(self explanatory - they need experience)
8. What is the GTM/sales motion to get to the person in the customer most impacted by the critical problem?
9. What other business challenges are involved with the solution?
10. What is the demo? What is the sales talk track? Who is the buyer? What will be the objections of the operational team?
11. Who are the competitors? Which of them is good? How much traction are they seeing?