You need to get some stud extractors. You drill a small hole on the broken sted and then screw the extractor in but it has a left hand thread so when it grips it starts to turn the stud.
To be honest if you can get the door off I would take it to my local engineering shop and slip them a tenner.
If its very dusty I use on of these
http://www.axminster.co.uk/product-Trend-Airshield-Pro-719697.htm
Its lovely on hot days aswell cos it blows cool air over your face.
A furring is a tapered wooden strip commonly used to give a fall on a flat roof joist. I've never seen a metal one nor can think why it would be appropriate in this case.
ttp://www.woodfit.com/product_info.php?cPath=115_15&products_id=193&Name=Cabinet+Hanging+Rail+-+2.5mt.+-+Steel
They are available cheaper elsewhere but at least you know what to look for now.
What type of windows do you have now ie sash or casement and what type do you want them replacing with.
I doubt you would get a breakdown for labour and materials, I know I don't.
I've just realised I wrote a bit wrong, you feed the router from the left to the right not from the right to the left because the cutter is spinning clockwise.