1) Version development. Like the far more compact X-Wing design. (Don't forget the variety of Tie Fighter, Tie Bomber, Tie Interceptor, etc from the Original Trilogy... There'd be bespoke versions, and especially learning from the issues seen in the OT.)
2ii) I suspect that the explanation for the visibility is that the 'hyperspeed bubble' of starstuff/energy-derived-from-starstuff leaks an amount of starstuff/whatever. ISTR that as one explanation why the laserbolts (actually plasmabolts... Star Wars universe tends to easily get mixed up over the difference between the two; I blame the translator microbes) are visible in prior space-battles.
...I'm more concerned about the the beams apparently going at handily visible speeds1 (seen mid-way, the - presumably superliminal - flyby appeared to be similar to the side-on view at the target system)... perhaps that was just a choice (and/or happenstance) of viewpoint distance in each case, being roughly equivalent. But then the view from the target worlds of a superluminal incoming quantity of (a fraction of) a solar-mass-worth of energy would have been... nothing! The destruction would advance faster than the light from the destruction. Only hyperspace sensors (or remote sensors communicating the passing events via faster hyperspace-channels) would give warning, not naked-eye observation. Unless the hyperspace bubble is formed to collapse just before its target, perhaps, the rough equivalent of coming out of warp (or a Farscape/Andromeda-style FTL-tunnel route) just before the destination.
And then you have to consider how it can be 'seen' from the side, unless you're within maybe a few light-seconds of the path as well. Oh, I don't know. Perhaps the hyperspace-escaping energy is still capable of radiating (even perpendicularly to the flight-path) at hyperspatial speeds before dropping out in a visible way at all observable points, and then decaying away (similar to neutrino-switching behaviour?) so that it it does not become an overly-long light-echo from all points between the original escape point and the observer, as they gradually (over the years) arrive like a whole set of photonic "Picard Manoeuvres" visible to the overly-patient onlooker.
1 Not "sublight"; still supralight, but at a convenient angle-or-arc across the sightline. Usefully also it's visible from that location on the planet. It'd be a 50/50 chance of not even being significantly over the horizon (or less likely, given the Lake District-style locale, with hills up on all sides), but it actually seems to more or less pass overhead, which is good for plot reasons but highly unlikely for any given random point on a random world that alreadi sits just off the path of the weapon-trajectory. By Star Wars terms, that's downright fortuitous (from a scene-setting POV) given that it seems that we have pretty much most of the far-far-away galaxy to play with when settling on the three respective locations required in that scenario...
2i) [going back a bit] I remember seeing the bolt as already split, whilst being watched from the bar-planet. I was assuming that the strands would merge (like the separate tributary beams merging at the 'tip' of the Death Star superlaser, which lasers wouldn't normally do, furthering the evidence that they're really plasma beams carefully corralled and aimed to merge into the main beam). But they didn't, they'd obviously been split at source (where they were effectively in the same blinding mass), extruded in virtually-parallel streams from the source pipe like mincemeat through a mincer out-pipe, such that they'd eventually impact the destination. [edit: each to their own destination... the barely discernible difference in original angles (theta and phi) being such that each deadly clump of energy impacts the desired destination pretty much square-on. Which requires both a masterwork effort of celestial surveying and an immense degree of control over the respective fractional-stellar energies at the point of launch. But then an organisation rooted in an old all-powerful Empire (neé Old Repuplic) that was still capable of amassing the capability to create the sun-sucker/spit-it-out-again weapon probably can be assumed to have a pretty formidable amount of resources and expertise, at hand...]
2iii) I'm not entirely sure, but either a only a fraction of the sun was used at a time (the entire energy not being necessary/practical), the planet was equipped with its own hyperspace generators (moving to a new, probably nearby, source-sun for the second shot)
3) Star charts won't (for the naked eye) be visibly different until the last light from the gone-star no longer reaches observers further adrift. (Gravitation probably also travels at SoL, because it's the top-speed of everything, saving those things that are artificially driven at FTL speeds... and maybe those rare natural processes that showed the long-long-ago civilisations that FTL was possible.) But we've also seen that star charts can be altered (prequel trilogy), if necessary, and they probably will have gotten around to replacing Alderaan with an asteroid field after not too long. (If not already, thanks to efficient Imperial bureaucracy... the Falcon probably doesn't update its TomTom too frequently, with such presumed-immutables as star-system configurations, unless docked in a safe harbour where the computer can pick up torrent packets with navigation deltas to update its current knowledge.
...indeed, I'm far more concerned that R2 had all-but-a-bit of a galactic star-map (that bit being the zone that BB8 had exclusive access to), which would seem on past form to be something universally known (fine details about the 'rim', excepted) and certainly of great interest. At least the prequel trilogy only had a single missing system, from every databank that counted, by one devious means or another... It would be easy to miss that without realising you were missing it.
4) I'd say that by that point the Resistance had observed the original attack. And with Finn's information further knew what they were looking for. And obviously have access to superluminal scanning methods. Not so sure I worked out how the First Order suddenly knew where the Resistance were... or suddenly cared enough. Although I gathered that their attack upon the New Republic/whatever worlds was because they were somehow protecting the Resistance. Perhaps politically, perhaps militarily. They (the Republic) may have had the wherewithal to launch a more powerful attack upon the FO's superweapon-world, at least before they ended up being castrated by the first attack.
...there wasn't much explanation about the state-of-play that appeared to have a viable post-Emperor version of the Republic, a viable Empire-Continues organisation that is the First Order and the rag-tag bunch of future-rebels that are the Resistance. Yes, you could go and look in the (original) Extended Universe post-Original-Trilogy novelisations (give or take the obvious changes), but the film never did (yet) explain this state of affairs in isolation, as far as I'm concerned.