1. At the smaller scale, couldn't the Romulans fire at these Starfleet outposts from their own planet? The Plasma weapon had a very long range.
Actually they made a pretty big deal about the plasma weapon having a natural range limit; indeed, the Enterprise uses this to their advantage by firing at the Romulans from outside their firing range (and Stiles says "A phaser hit at this range would be the wildest stroke of luck!")
It's implied to have the ability to travel at FTL velocities, but the warp speeds shown in this episode are depicted as being (as is often the case in TOS) remarkably slow, not necessarily even FTL. As we've seen, this only ever happens deep within planetary systems well within the range of a star's gravity well.
Probably on the other side of the system right now.
4. If the Romulans have been circled in for a hundred years, shouldn't Starfleet Intelligence have some good visuals on any Romulan ship design prior to the introduction of the cloaking device?
Possibly, but at that range not enough to tell more than indistinct shapes and power emanations. Enough to make a rough guess, but little more.
5. Wouldn't the "stars of home" look the same on the other side of the neutral zone to the Romulan Commander if the fight took place in their own star system?
We've been assuming that the Bird of Prey's mission was to test Federation defenses by attacking those outposts with its new weapon. But we don't really know that for sure, do we? Fuel was definitely an issue at this point, but we also don't know the bird of prey's actual flight range; Hansen did, after all, mention that the Romulans had destroyed outposts Two, Three and Eight
The first are understandable. Outpost two spotted the BoP on the way back through the neutral zone and immediately radioed its neighbors for confirmation. The Bird of Prey destroyed outpost three with a single shot, but outpost four survived long enough to get off a message to the Enterprise. But when in the hell did the Romulans hit outpost eight, and WHY? I'd guess that outpost eight was destroyed first -- they blew it up on their way OUT of the neutral zone -- and which would have prompted Starfleet to send the Enterprise to see what the hell as going on. A couple of days later, the bird of prey makes its return trip and doesn't have enough fuel to keep the cloaking device active. They got spotted WELL before outpost two's defensive perimeter and that gives the outpost enough time to call its neighbors, who are then also
destroyed to preserve the mission's secrecy.
This was probably a spy mission gone horribly wrong: possibly deep-space reconnaissance of Federation worlds, but more likely, the Romulans were delivering a spy (or spies) into Federation space, disguised as Vulcans. The need for secrecy would be understandable: nobody knows the Romulans have a cloaking device, and even if they did, nobody ever suspects a Vulcan of being up to no good. Vulcans, after all, do not lie.
That, finally, would explain why the Romulan Commander in "The Enterprise Incident" seems to know so much about the Enterprise and its crew. They've been infiltrating the Federation for years already and Starfleet was none the wiser until one of their spy ships got shot down trying to cross back into the zone.
6. Couldn't Starfleet then start shooting at the Romulan homeworld from their outposts as a response since they're at a close enough range.
Not with phasers, no. They'd probably have some kind of long-range cruise missiles or something similar in the event of the outbreak of war, and Romulus would also have similar long-range weapons. But as I speculated above, destroying the outposts may not even have been the point of the mission.
Here's a thought: the Centurion says to his commander "We've seen a hundred campaigns together and still I do not understand you!" For all we know, this isn't the first time this particular commander -- or even this particular ship
-- has crossed the neutral zone. It's merely the first time they've ever gotten caught.