shuttles often had warp drives even on TOS.
Yes, but their Warp speeds and range are frequrently touted as 'limited'.
Type IV shuttle in VOY is limited to Warp 4. Sure, there was a shuttle Tom Paris used to break the TW barrier, however, I don't think this would be standard practice - or, SF could simply use a same technique to reach incredibly high Warp speeds without breaking the Threshold - the thing is that maintaining those speeds would probably be extremely difficult because the power requirements at higher Warp increments past 9.9 would go well beyond of what a shuttle could sustain for a significant enough portion of a time (power consumption and speed usually DOUBLE past 9.9 with every increment),.
I always assumed that at Warp 10 though, the bussard collectors were able to pick up the energy from subspace and keep the shuttle powered and that once you cross the Threshold, the energy needed to sustain it was lower compared to what was needed to actually break through the Threshold (however strange that may be).
So, I don't think a shuttle would have been a viable option to transport Gwyn all the way to Solum (which is in the Delta Quadrant).
It would need to cross thousands of lightyears to get there.
Earth is 25 800 Lys from the galactic centre.
Since its been established that Solum is 'somewhere in the Delta Quadrant', even if it was near the border of Beta and Delta, and given the fact the Vau'N'A'Kat still hadn't made FC, it would imply they might be situated in a remote sector of the DQ that no one besides the UFP had any plans on visiting, and the distance in question would still be greater than 25 800 ly's.
So, if a ship were to use Warp 9.9 to get there, it would reach solum in over a year. Add 9.91 to the mix (which would be double the speed), and you cut the journey to around 6 to 8 months perhaps - and I don't know if SF is able to maintain 9.92 on most ships just yet).
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.
Or, Solum is located in a REMOTE sector of the DQ that no one besides SF deemed necessarily worthy to explore and Solum was fairly isolated from other Warp capable species.
VOY was heading in a relative line path back to the AQ... and its deviations from its original course may have been by dozen LY's at most... so, its likely Solum is a fair distance away from Earth.
Earth is 25 800 Ly's from the galactic centre... since Solum is somewhere in the DQ, it could easily be a larger distance (than what I just said) away - and for that, you either need Slipstream, or a ship capable of reaching and sustaining Warp 9.91 that would get there in about 7-8 months (or 3.5-4 months if its capable of sustaining 9.92 - which is certainly possible, since the Prometheus class was already capable of sustaining Warp 9.9 effortlessly in S4 of VOY. Given that its been 8 years since then by the time PRO S1 finished, its possible SF managed to increase 9.9 stable cruise to 9.91 or 9.92.
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.
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?).
Yeah... its likely SF would in that case use a shuttle with some kind of stealth system (perhaps the one which Endgame admiral Janeway brought back and SF deemed is 'premissible' to use on a covert mission when necessary) to beam Gwyn down to Solum in the city she saw in the holo (which seems like the most likely place to find her younger father).
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.
Ascencia mentioned the Diviner was similar in age to her (when FC occurred)... since then 'years and decades' passed (during which time a civil war erupted).
Given that Chakotay was stuck 52 years into the future (and been with the Vau'N'A'Kat for 72 days), the Diviner would have been approximately 70 odd years old by the time Chakotay launched the Protostar back into the past.
70 years old and looking particularly well (in Vindicators memories) at that age makes sense... then add another 17 to over 20 odd years to that while he was searching for the Protostar in the past and he'd be in his 90 - ies by the time PRO began.
If he was really that age when PRO started, then it would make sense he needed a bio fluid to sustain him most of the time and developed a limp (possibly due to old age) - and why he made Gwyndala in the first place (because he knew he might not be able to live for much longer and he wanted (desperately) to complete his mission.