Those early ships weren't long range explorers, since NX01 was the first, and had to trundle around at about warp 2 so getting just from one star system to another would take months. So I imagine hanging around earth (or the first colonies) patrolling for threats was one of their major duties. Basically I'm agreeing with your earlier statement that 22nd Century starfleet also had a military role.
Depends on where in the solar systems those ships were at the time. Assuming the timeline is accurate, it is February 14, 2154. If ships are stationed anyplace but Earth, at Warp Factor 2 it will take several minutes to arrive once a warning gets out. The Weapon seems to cause some interference with communications, though how powerful it is is unclear. Archer's group has something like ten minutes to stop the weapon. The High Speed Andorian ship makes it in time. The Vulcans would seem to be out of position. Maybe it was not logical to them to be that close, or they had issues due to the Andorian ship? But for the Earth ships...
Mars in on the opposite side of the Sun on this date. Over 2 AU away and with a stellar body between Mars and Earth. Without the stellar body it would take a Warp 2 ship over two minutes to reach Earth. With having to go around the Sun, three minutes?
Venus is on the other side of the Sun as well and is 1.5 AU away. So given the manuever, two minutes away as soon as they get a warning.
(It is unlikely they would have ships at Mercury, though it is only 1 AU away so only a minute at Warp Factor 2)
Jupiter is also on the other side of the Solar System from Earth and is over 5 AU away. At Warp 2 that is over five minutes away.
Saturn is near closest approach to Earth, but is still 8 AU away, so any ships there would take just over eight minutes to reach Earth.
Ships that are any farther out that can't make better than Warp 2 will not make it to Earth before the planet is destroyed. Even at Warp 3 it would take 9 or so minutes to get to Earth from Neptune.