How to use data to come up with estimates for tasks at the initial stages? What's a reasonable time to come up with the estimates themselves (if there's research involved)?
The easiest heuristic here is just to pattern-match on historical data. If you're doing project X, find something that looks similar to project X in the past year, and that should be the starting point for your estimate. See Alex's great answer here.
The question of a reasonable time to come up with estimates is what I refer to as "a date for a date". This is a great practice of doing some legwork to better scope and understand the project. A few inputs for how long this should take:
If you feel like you don't have enough context, check out this detailed discussion.