Already defeated these arguments, i've never seen such a desperate attempt to grasp at any straws available, imaginary or not. It's very amusing.
1. The ship doesn't exist any more because, you know, it got erased.
the matter that the ship was made of got erased. The designer was not erased. You see him at the end and a pad on his desk showing the same visuals that were on the time ship. It's unclear whether another one was made or not.
2. Star Wars ships do actually have a kind of temporal shielding. It would be foolish to simply assume that the Krenim's now-erased weapon on the now-erased ship will simply be able to bypass this.
a specific type of temporal shielding is required. If this relativistic shielding is considered temporal shielding, it's the weakest type of sheidling ever made. It can block energies in hyperspace, not changes in history.
3. I've been having a look at the Memory Alpha page on the ship in question. The now-erased ship was slower than the USS Voyager at Warp speeds, meaning that it would to take decades to get anywhere in the SW Galaxy, whilst all those Star Destroyers cross the galaxy in mere days. I say would because, of course, it doesn't exist any more. Note, by the way, that whilst its travelling at snail pace through the galaxy, the locals will be pouring their resources into developing a means of defeating or withstanding it. Or would be, if it still existed.
since the crew don't age, taking decades to get somewhere is not a problem. They can also erased targets on a regular basis on the way there. After each incursion the locals would lose their memories of what is happening and not bother trying to find ways to defeat the weapon. Example: if the ship erased 1 planet the locals wouldn't worry because nothing was erased as far as they know, then another planet gets erased and still nothing was erased as far as they know, etc.. no cause for concern.
4. It needed to enter the atmosphere to fire its weapon against a colony. How would it get through the planetary shields at, say, Coruscant? Do you have proof that its now-erased weapon (or indeed, hull) can bypass Star Wars shields when it can obviously, for example, interact with regular matter? If it has to fire from within a planet's atmosphere, and can't get there... yeah...
their weapon is temporal and phased out of space-time. The weapon would fire like it wasn't even there. Plus the ship should be able to just fly right though the planetary shield since it's phased outside of space-time. Any attempt to prove otherwise is only attempts to prove that star trek is fiction which you would have to be delusional to not already know that.
5. Related to point #2, Star Wars powers obviously have some good knowledge of how time works. We've even had good old time travel in the EU.
All incidents of time travel in star wars are only partially documented and due to unusual hyperdrive malfunctions, the effects of the Force, or similar exotic events. Usually people like this insert the word "obvious" in a lame attempt to try to pass off a point as obvious. If they had good knowledge of how time worked they would have temporal shielding and would resemble the federation in the 29th century with their technology to scan time and travel to any point they wished. The krenim know more about temporal science than star wars does yet the krenim ship was able to alter the krenim imperioms history and even the krenim imperium wasn't able to do anything about it.
6. Star Trek time travel (and similar phenomena) seems to work on a "many universes" or "parallel universes" model. Which would make the Krenim ship more of a fancy means of hopping between parallel universes than one that actually buggered up time. Which means whilst it's traveling between universes, Star Trek is getting screwed over.
in some cases it does like in the new star trek movie. In this case it doesn't. They change the current timeline that they're in, they make that quite clear. It's similiar to the models of time travel shown in the "yesterday's enterprise" TNG, TOS: "The City on the Edge of Forever", Star Trek First Contact, "Future's End" voyager, etc...
7. The last I checked, quite a few species (humans included) don't have a recorded homeworld in Star Wars. Those worlds that are suggested are all core worlds (see point #3).
I think I read somewhere that humans were abducted and transported to the star wars galaxy where they colonized the planets. In my scenario, Q transports them there. Naturally star wars and star trek don't interact. In the verses debate we operate under the premise that the ship is in star wars space in order to make the confrontation possible. This objection is refuted by accepting the premise in the hypothetical situation.
8. I haven't watched the episodes related to the ship in some time, but I believe it could communicate with others whilst its magic shields were up. It this is able to interact with normal space-time on at least some level, so its shields aren't all they've cracked up to be. I also notice that, as per your quote from Harry Kim, Federation sensors were able to detect it, and it was clearly visible to the naked eye even! Proof that this will protect it from, say, Palpatine force choking the crew (not that it's important of course: the ship doesn't exist any more)? Also provide proof that it can avoid the other exotic weapons Star Wars societies have available.
Doesn't matter. Star trek writers give the vessel the characteristic that it is impervious to weapons from being phased outside normal space-time. Any attempt to find inconsistency in these properties is just an attempt to use a proof of star trek being fictional to prove that the krenim ship is not phased outside normal-space which contradicts star trek canon. If the vessel wasn't outside normal-space then the crew would have shown signs of aging after 200 years, they wouldn't keep making references in the episode that it was outside space-time and the ship would have taken damage when it was attacked while the temporal core was online.