Is the estimated mortgage on Trulia accurate? If not, how much can it vary?

No. They are based upon teaser interest rates to gain your interest and motivate you to apply for a mortgage with their lender. You will likely be paying a higher interest rate, higher home owners insurance and higher taxes. Plus its based upon paying the asking price when most buyers can negotiate a lower purchase price.

It just gives you an 'idea', you would need to go and see your own bank/mortgage lender to get a true cost

They can vary widely depending on credit, down payment, term and so forth. Also, sometimes those figures include property taxes, other times they don't.

Yes, pretty accurate. Rates depend on how much of the sale price you have to borrow. Since sub-prime mortgages caused the worst recession in '08 since the Great Depression, the mortgage rates are pretty much set, although some lenders can give a slightly lower rate.