Can the owner of a repo see clones?

As far what I found you CAN'T know when someone clones it (if you mean exact time) nor who cloned it. But you can know how many clones were made on which date and the number of unique cloners from ths url.

https://github.com/{usernamme}/{reponame}/graphs/traffic

Insights tab:

However one thing I find fishy is unique cloners is more than unique visitors, how can someone decide to clone even without visiting the repo. I guess it may be bots in such cases.

You can use clone graph on GitHub to find out how many times your repository's source code is actually cloned in a given day. More information can be found here https://help.github.com/articles/about-repository-graphs/#traffic

The question is too general, but let me answer the question as it stands now.

Can the owner of the repo see when someone clones it?

No, they cannot. If I go to one of your repositories and clone it to my local hard drive, the owner will not be able to view that activity. And why would you want to? Likely there are many clones of your repository.

Know that clones can live on other systems than GitHub.

Now, will the owner know that someone forked their repository on GitHub itself?

Yes, they will, assuming they pay attention.

I did the following:

1. Logged in as my main account
2. Created a repository
3. Set up a new dummy-account on an alternate email address
4. Forked the repository I created earlier
5. Logged back into my main account

This is what I see on my first page after logging in:

If I do the following:

1. Click on my repository

2. Click on the small 1 to the right of the "Fork" button:

   

3. Click on the "Members" tab:

   

4. Then I see this:

   

Conclusion:

Yes, the owner of a repository will see when someone makes a fork on GitHub, but no, they will not see it when someone makes a clone somewhere else.