Click the question to show/hide the answerIs it possible to extract to PDF or TIFF and generate the XML extraction file at the same time?

Yes. You can export to an image format or PDF and at the same time extract text fields to XML, Comma-Separated, or Plain Text format. These fields can be defined on a per-document basis or there can be a default set for each directory in which input files appear.
Click the question to show/hide the answerCan I do this in automatic mode from a watched directory?

Yes. To create TIFF and XML simultaneously you need to define a field covering the area of interest. Then in the Options|Configuration dialog select the input file specification, select TIFF output, and possibly give an output specification if the default is not suitable. Then click 'Image options' and in the Log File section choose 'XML' as the format and 'All fields'. Click on the Automatic tab and enable the timed check for files, e.g. every 5 seconds.
Click the question to show/hide the answerWhat about logging (page counts, etc.) into a database as well?

The file logging mechanism is not currently available in conjunction with the field extraction.
Click the question to show/hide the answerCan EscapeE create XML style sheets in addition to creating the tagged XML data?

Yes, since version 4.70: see Exporting XML data fields.
Click the question to show/hide the answerI defined a number of fields through the page view method, but when I ran the XML export I only got the page numbers and no additional data?

It's possible you inadvertently defined the fields as being relative to a tag which did not occur on any of the pages. Another possibility is that you asked to output only the selected fields and failed to select the fields you require, see Exporting XML data fields.