Hi! Timestamps for each annotation as it's submitted in the UI is a feature coming to Prodigy v1.11 – we'll be releasing a new nightly soon that will already have it 
In the meantime, here are some ideas and code snippets you can use to add it yourself: Feature request: timestamps for data entry - #5 by ines Quick note: you probably want to use Math.floor(new Date().getTime() / 1000) for the timestamp so you can easily use and convert it in Python.
There's no direct feature that outputs the progress over time, but if you have the timestamps, you should be able to easily calculate that, depending on your task, the datasets you're tracking and how you define "progress". Using the Database API in Python you can load all examples from one or more datasets, get their timestamps and then group them by timestamp rounded to week, month, year or whatever else you're interested in. You can then output the number of annotations created in the given time period, or a cumulative sum of all annotations, which is more like a classic "progress" diagram that's always going up. Or you could look for other patterns if you want, like most active day of the week, most active hour of the day etc 