Regarding your grant:
1. How many outstanding shares (including as yet un-granted option pool shares) - divide your grant by this number and you have your ownership share of the company
2. If you're granted RSUs, ask about whether you need to file an 83b
3. If you're granted options, ask for the price of these options (or the last common share 409A valuation). This is your cost value of each share
4. Post-money valuation of the previous round (can't be calculated by 409A since that's different, but rule of thumb is that 409A valuation X outstanding shares x 5 ~= last round valuation).
5. Post-money valuation/total outstanding shares is technically the paper-worth of your options or shares (and you can subtract the 409A valuation to get the current expected profit per share). Assuming nothing else, your shares vested per year X (valuation-409A valuation) = your paper equity salary per year
Regarding the company prospects:
1. Money in the bank
2. Monthly burn rate, at which point you can derive the amount of time left for the company to keep going without raising more funding
3. Revenue growth rate, and expense growth rate - this allows you to adjust 2
4. Status of next funding round - when, and which investors. Ask if the same investors will participate again in the next round of funding. Very very rough rule of thumb - if yes, company is doing ok. if no, something's up (with the exception of large growth rounds where smaller investors can't participate anyway)
5. Ask about liquidation preferences (so if there's a sale or exit, do investors get their equity share or at least 1x their money back (the higher of the two), or do they get a multiple of their money back (if that's greater than their equity share)
*Edited formatting