Its also possible that Gwyn was only on the shuttle to rendezvous with a SF ship that will get her to Solum (perhaps a Slipstream powered ship or a Prometheus class capable of sustainaing Warp 9.9 effortlessly which would allow speeds of 21 473 times speed of light (or perhaps even 9.91 which would be double the speed).
That's what I assumed right away - I can see the ship being the (hastily repaired) Dauntless, so Tysess and Noum could be on board and the already created CGI environment could be reused for S2 - but a surprising (to me) amount of commentators, bloggers, podcasters seem to think she has the shuttle and that's it. And the existence of transwarp conduits makes it possible for her to reach Solum theoretically, though it would still take a lot of time (due to the inbetween travel at regular warp, where a shuttle is likely not going to be near a fullsize starship in speed) and be risky given the other ships who make use of it.
Though if they sent her in a shuttle, its possible they had an alternate way of sending her to Solum (like you said, perhaps via a TW conduit, maybe even a subspace corridor if SF was able to finally detect them - and I don't know if Gwyn would have been allowed to keep the shuttle which the Vau'N'A'Kat would analyse - but who knows).
If they send Gwyn alone in a shuttle, then I agree they would have to assume the Vau N'akat are likely to get their hands on it. Would seem very sloppy from Starfleet, like they don't really care about the mission or about their tech getting "misplaced".
Gwyn could more or less easily convince the young version of her father she is who she is (via telepathy perhaps).
If that works as seemed to be implied in "A moral star", yes, he should be able to tell she is completely sincere. That would be the obvious place to start. And another point where a Starfleet crew, preferably experienced with studying alien worlds, could help: locate where she can find the Diviner. I'm not sure Gwyn otherwise would be able to find him, given she seemed to know next to nothing about Solum before "A moral star". Unless he gave that info (where did he live, what was his function, etc.) telepathically when he died, I don't think she knows where on the entire planet she needs to look.
But, I already got the impression the Vau'N'A'Kat already had Warp capability and starships - it seems unlikely they would be 'close to warp' and then decades later come up with 100 ships after the aftermath of their civil war to send after the Protostar.
The Vindicator mentioned they took their last 100 ships and sent them after the Protostar... implying those ships (and more) already existed by the time of FC.
After First Contact, they could have had help from the Federation (since the Vau N'akat are pretty advanced in some ways, they may have been open to help with propulsion, possibly in a trade with Vau N'akat tech they wanted) and/or bought technology from, say, the Ferengi (or even the Kazon, whomever had relatively advanced warp vessels and was willing to sell for a more or less reasonable price).
It is of course possible they do have warp already, but if they think they are alone they can't have gone far or have been at it for very long.
I don't think the line of Ascencia indicates in any way those ships must have existed before FC. Many of them could have been build in the run-up to the civil war (arms race?) or even during it.
That depends. If the Vau'N'A'Kat detect one of their own onboard a shuttle (As opposed to an alien), this (alongside her plea for saying what awaits Solum if they don't unify) could be enough to shift things into a different direction (which would definitely confirm that the future in which Chakotay is located in is indeed an 'alternate one'... and even perhaps take some of the younger Vau'N'A'Kat from the Prime timeline to accompany Janeway and her crew through the anomaly to the alternate future timeline to help convince them the civil war should end and that the Vau'N'A'Kat need to be able to slavage what can be salvaged and move on).
One of the things Gwyn could propose to the present day Solum is that they delay proposal for entry into the Federation until they manage to deal with their own division that would inevitably erupt before they are ready... and only try to join when they deem themselves to be ready (understanding that SF cannot realistically interfere into their internal affairs and this decision needs to come from unified Solum.
True, but it would still mean they learn about the Federation and its values, likely aqcuire Starfleet technology (as Gwyn's shuttle would likely be taken, even if only to examine it to corraborate what she says) and learn they are not alone. Starfleet could as well make that first contact themselves then, in that way (with or without Gwyn as "living proof"), and say they wouldn't accept any proposals until the Vau N'akat can prove their society is sufficiently unified not to fracture and fall apart over potential membership or alliance with the UFP.
I wonder, how old was the Diviner supposed to be? Could there be a young version of him already living on Solum?
It was implied in the last scene of Dal and Gwyn together, that a young version of the Diviner lives on Solum in the present (said, by Ascencia, to be "a bright young leader" at this time, though what his exact position is remains unknown, perhaps akin to an up-an-coming young politician?).
As to his age, I think the Diviner was shown in one of the "murals" in Ep 16, showing the arrival of the Prometheus class vessel on Solum. He looked fairly young there (possibly with an equally young Ascencia also in the frame), but I would guess more in his twenties and thus a number of years older than Gwyn). First contact is likely to have occurred, in the Diviner's original timeline, shortly after the present day. That would be why the Diviner - and later Ascencia - were in a hurry and felt that time was running out for them.