You are on the rite track to getting this implemented. The first thing you mentioned about concatenating the first and last names can be done with the recordset query itself. You can concatenate two columns in the sql like this:
SELECT CONCAT(firstnamecolumn, lastnamecolumn)
To get the pages working together you should think of your page where you are selecting the users from as your search page. It will post the results of the form to your second page which you should think of as your results page.
You will have both UE and DataAssist Search applied to this second page. When you configure the DataAssist Search you should specify the trigger as the submit button from your first page. For the search criteria you will select a list type search then select your target list from the first page with the users that have been added. You will be searching the id column from this users table.
That should be about it for the search. This should give you a recordset on the second page that holds the details for the users that were selected in the list on the first page.
Lastly you will just add in the Universal Email server behavior to this page to send the form details to these users. The trigger for the UE should be same page post. The recordset should hold all of the same values for you and each listed person will get an email. Post back if you have any further questions or need more advice on this.