The Baby Taylors should use light strings per Taylor's recommendations.
You can find info on adjusting the truss rod if necessary at
http://www.taylorguitars.com/global/...adjustment.pdf
Test it using the method listed (hold down a string at the 1st and 14th frets and put a business card at the 6th fret. The string should be just touching the card or very slightly above it. If that is the case, the truss rod doesn't need to be adjusted.
Here's a link to adjusting the action by altering or installing a new saddle
http://www.taylorguitars.com/global/pdfs/action.pdf
The two screws are to remove the neck to put in or take out shims to raise or lower the neck from the body.
My BBT doesn't have any wiggle in the neck with the strings off so I suspect there is something not sitting correctly in the neck joint. I'd call Taylor support 1-800-943-6782 8AM - 4PM PST M-F and explain what you are seeing. They can probably help you out fairly quickly.
Hope this helps.
-Jim