Transcript from First Contact (after Picard returned to the ship after inspecting the Phoenix):
PICARD: Mister Hawk, before we lost internal sensors what were the exact environmental conditions in main engineering?
HAWK: Atmospheric pressure was two kilopascals above normal, ninety-two percent humidity, thirty-nine point one degrees Celsius.
PICARD: Thirty-nine point one degrees Celsius. ...Like a Borg ship. They knew their ship was doomed, our shields were down and somehow they transported over here without being detected. They'll assimilate the Enterprise, and then ...Earth. ...Picard to Riker. ...Enterprise to away team. ...Respond.
- Why would the Enterprise have its shields down when it was just
engaged in a huge battle with the Borg and was still pursuing a Borg
Traveling through the temporal wake took their shields down.
Transcript from when the Enterprise first gets through the temporal wake:
RIKER: Shields are down. Long-range sensors are off-line. Main power's holding.
- Even if the main shields were down, doesn't a ship normally have its
deflector shields up? Wouldn't this be enough to prevent the Borg
Riker reports the shields are down, one could assume this meant all shields, including the deflector shields.
Edit: I forgot when writing this that the main shields were different from the deflector shields. Deflector shields are designed to protect a ship against particle impacts at high velocity (ex: traveling at warp speed) and could give some basic protection against weapons. The main shields, which are much more powerful and used in tactical situations, are the ones that have the ability to block out transporter signals. So even if the deflector shields weren't down, they may not have been strong enough to block transporter signals.
- Is there really no security system in place to prevent intruders
from transporting aboard (especially when all Borg are bad)?
Yes, the shields :)