to plug the hole get one of these:
80 Watt Iron Plastic Welding Kit TPO TEO PP Rod Mesh Auto Car Welder Repair Kit | eBay
and use a piece of plastic from the muffler you just cut off.
there may be info on removing the intake manifold here:
Porsche Boxster 986 (1997-2004) / 987 (2005-2008) Technical Articles | Pelican Parts
otherwise workshop manuals are here:
Manuals_Original
only the driver side manifold has to come off. I couldn't get mine completely out because of the aos tube, but was able to move it to get enough room. use your dremmel to cut the old airbox into pieces to get it out. the new one will go in with some contortion - to make your life easier, saw off the tab at the back of the engine compartment lip as per reebuck1, and bend the driver side tab for holding the engine compartment lid out of the way.
there is no oem tube to join the airbox and the throttle body. the 987 airbox is designed to work with the 987 plenum which has a big bend in it. the plenum you are using doesn't. you will either have to fab your own, or check with ipd - they make a tube that will join a 987 airbox to their plenum (which is about the same geometry as the one you are using).