What's wrong in my rule for sending e-mails using VBO?
Obviously "something" is wrong in what you're trying to get to work. I suggest you enable the typical the Rules debugging (to find more details about what's happening and causing your error), as detailed in "How can I display the value of a variable inside a condition?". If needed, add a copy of the Rules execution log as an update to your question.

Maybe also checkout the tutorial "How to process the results of a VBO enabled view via Rules?".

Plan B

A possible alternative that should work also, is to get the Views Rules module involved in the puzzle you're trying to solve (instead of using VBO). Some details about this module (from its project page):


  Provides Views directly as Rules actions and loops to seamlessly use view result data.


If you're not familiar with Rules (yet), the previous quote may seem a bit cryptic (it may make you think like "so what, how can this help me?"). Therefor some more details about how to move forward using these modules:


Create a view (using Views) so that you have 1 Views result (row) for each user to be eMailed, whereas that view has fields (columns) for each of the fields that you want to use to create your eMail. So your existing view could already be pretty close (if you just remove the VBO field). Important: use a Views display type of "Rules".
Create a custom rule in which you use the Views Rules module to iterate over each of these Views results in a Rules action, using the Rules technique known as a "Rules Loop".
For each iteration step in your Rules loop, perform a Rules Action to ... euh ... right ... Send an eMail. At that point you'll have all data from each column of your Views results available as so called Rules Parameters. So at that point it's a piece of cake to create an appropriate eMail.
The only remaining thing is to decide about the Rules Event to use for this rule to be triggered. But that's up to your own imagination (any Rules Event will do). In your case: your existing Rules Event should also be fine. Optionally, you may also want to add whatever extra Rules Condition(s), also up to your own imagination.


Easy, no?

PS: I'm assuming this question is about D7 ...