How do you estimate a task with unknown parts?
Timebox the unknown separately. Estimate the known work normally, then add an explicit investigation slot with a decision point at the end. Merging the two produces a number that is wrong in a way nobody can inspect.
One offer has more cash, the other more equity. How do I compare them?
Value the equity at zero and see whether the decision changes. If the lower-cash offer still wins on work and people, the equity is upside. If it only wins with the equity counted at face value, you are being paid in a lottery ticket priced by the seller.
How much notice is reasonable when the handover is complex?
Whatever the contract says, plus a written handover that outlives you: runbooks, access list, the three things that break at 3am. Extending the notice period rarely helps; writing things down always does.
How long does this usually take in practice?
An afternoon to do it properly the first time, then minutes when it recurs. Most of the first afternoon goes into discovering which of the defaults do not match your situation.