Implementing 1000BASE-T (Twisted pair) over PCB backplane
1) yes, you can. 1000BASE-T (MDI) is suitable for doing this. but keep in mind that:


you does not need a separate ground "under" each 1000BASE-T MDI (= a couple of four pairs matched), one plane "under" all of them may be enough. the main tip here is that plane must be tied to chassis and topologically separated from any local ground despite of such a ground is tied to chassis too.
the switch you referred to is a board level switch, "fanning" its 1000BASE-T MDIs out of the case directly (via passive MDI to "RJ" connectors) could be erroneous because of a possible lack of necessary isolation level (port-to-port, port-to-common_ground, and/or port-to-chassis) provided by the switch board itself.


2) UTP gives about 5-7 pF/m, STP gives about 50-70 pF/m. how much the board gives... i don't know and think you can calculate it yourself based certainly on your design. that will give you an answer about equivalence.

3) it is nearly the same as for 100BASE-TX MDI (the key word there is MDI) because both 100BASE-TX and 100BASE-T PHYs work over the same cabling - Cat.5 compatible mediums. yes, 1000BASE-T MDI has a stricter requirements - but slightly not dramatically.