Can you see time used on editing a project?

You pose a very good question. If you can't answer that question for yourself fairly accurately I can promise you one thing. You will have an extremely difficult time making a living in any kind of creative field. Time and resource management is critical to any kind of business. 

It is pretty easy to keep track of how much time it takes you to get something shot, especially if you pay people to be in and work on your movie. Work on a feature film that has a production goal of 5 pages a day and end up only shooting 2 or 3 and you will be looking for a job before the first week is over.

Post-production is another story. Most new editors and visual effects artists I have met in my 4 + decades in the movie business completely lose track of how long they work on things. They put in a lot of all-nighters and often need to ask for more time.  It is a very common problem. Software that keeps track of your time won't help you manage your time any better than trying to develop good work habits and organizational skills. Start making estimates. Tell yourself you have 2 hours to do that roto job and then see how far you have gotten in the first 15 minutes and adjust your workflow so you are going to be about halfway through the project in an hour. After you have done a dozen or so roto jobs you will be able to take a look at a shot and make a very accurate prediction of the time required. Do the same for all of your common tasks. 

Most of the time I finish a project a little ahead of schedule. That's how you make money. That's how you end up on time. The only projects that I work on that seem to drag on and on and on, are personal ones that I play with so I can figure out how to do new things. I always put paying work before experimentation. I also always devote a few hours each week learning better ways to use the tools I have. If you pay attention to your time and you start keeping a simple work record you will not have to ask or wonder how much time you spend on a project. You will know. If you do not start keeping track of your time you'll never know how long it took you to do anything and you will never really know how much to charge a client because the days of working post-production by the hour are long gone. 

Nothing automatic, but there are some manually-triggered "punch clock" scripts such as https://aescripts.com/timespan/

Hope I get you right.

One vague information about this is the creation date and last changed date of a project file. However, if the file was copied, the timestamps could be messed up (depending on OS and copy process).

Also, you can give it a try and open the *.aep file in notepad++ or any other IDE. If you are lucky, you'll find some readable timestamps. Don't give to much hope on it, for AE there is no need to store this information, so it's unlikely it will do so.

If you want to track your work, try a time-tracker software. I did used ManicTime a while and liked it.

*Martin