Mouse up inserts value (e.g. checkbox' name) at the cursor position in a text field of my choice.

You would have to insert the following script as an On Blur event into every text field:

var fldName=event.target.name;

Then insert the following Mouse Up action into the check box field:

if(fldName)

{this.getField(fldName).value=this.getField(fldName).value+event.target.name}

Every time the check box is clicked though, it will add it's name to the existing text in the text field.  Are you sure this is what you want?  You might want to test whether the text field already contains the check box name first like this:

if(fldName)
{
if(!new RegExp(event.target.name).test(this.getField(fldName).value))
{
this.getField(fldName).value=this.getField(fldName).value+event.target.name;
}
}

To add the script to every text field in the document, run the following script in the console:

for(var i = this.numFields - 1; i > -1; i--)
{
var oFld = this.getNthFieldName(i);
if(this.getField(oFld).type=="text")
{this.getField(oFld).setAction('OnBlur','var fldName=event.target.name;')}
}

No. You can't know where the user has clicked into the field and insert the text there.