When to use "click" and "click on"

Solution 1:

Generally speaking, click on is used for something virtual. You wouldn't say click on with your first example. Click on is used when you want to instruct someone to use a physical object (i.e. the mouse) to select a virtual object.

However, you can use click with virtual objects as well, it's just not as precise. "Click the link" would be OK, you are assuming that it is understood the mouse will be used to click the link, and are thus extending the property of the mouse (i.e. clicking behavior) to the link.

These aren't hard and fast rules however, at least to my knowledge.

Solution 2:

In the first 3 sentences both 'click' and 'click on' are ok, but why use the word 'on' when it is not necessary?

In the 4th sentence 'click on here' sounds strange. Preferable is: "Click here ..".