Why is the select link showing up under the [[Date] ] input field/box and not to the right of it?
because the field is hardcodedly enclosed in a div tag. If you want the select to the right of the field either put these items in a 2-column 1-row table or work out the required css (which may be quite tricky).
What is the JavaScript template for?
It is for javascript code, BUT, in your case you use [[Date#id] ] tag which is not javascript code and as is can be known and properly converted to code only in the Add template. You can pass this tag as string into a function which is defined in the js template but that requires some more coding. You also include a js file which you can do in the js template if you use the proper dom methods.
Is there a difference between going into HTML mode and disabling the editor?
If the editor in database 2.0 works like in 1.9, it doesn't appreciate white spaces in the code so unless you remove all white spaces from the code you need to disable it if you want to edit the template. As a workaround, keep and modify this bit of code in an external file and copy paste into the template as needed.
hth 