Regarding points 1 and 2, single rapier will be better as long as your accuracy is around 25 points higher than enemy deflection assuming no hit-to-crit other than the single weapon passive. Past that, the two attacks from dual wielding will result in more crits overall. If you're using your invocations and your parties' abilities to lower defenses or you're attacking paralyzed enemies, two weapons are probably better after the early game.
Regarding 3, the rapier modal and the small shield modal don't stack because we can't have nice things.
Regarding 4, as Elric Galad mentioned, sun and moon is excellent for building crits on a skald. The singing scimitar is also amazing for skalds since it lets you cast back to back top-tier damage invocations in every fight. Given the current balance, a rapier with the modal will probably beat sun and moon in phrase generation unless you already beat the target's deflection by a lot and you have a priest buffing you with devotions for the faithful (which also doesn't stack with the rapier modal, so reduces it's usefulness). Maybe this is possible if you've equipped the ring of focused flame and are spamming flames of devotion. Anyway, the flail also boosts either the power of your melee or the power of your spells, depending on the time of day. I think the singing scimitar will beat out any other weapon on a skald, since it effectively gives the effect of 6 melee crits for free, allows you to empower every fight and it's shocking lash applies to everything you do, including attacks with the offhand weapon and your spells.
TL;DR on the above, use sun and moon if you have a priest in the party, don't have a party member who wants the ring of focused flame more than your MC and you plan on spending most of your zeal on flames of devotion. Otherwise use a rapier. Sasha's Singing Scimitar is almost certainly the best skald weapon, unless there's some synergy I'm not aware of (e.g. disengagement riposte and AoE attack shenanigans with Whispers of the Endless paths).
Regarding 5, I imagine whatever good ranged weapon you have access to is fine for a back up. Late game, the wand of the weyc is beautiful for chanters, since it gives you +3 power levels after empowering an invocation. I don't know what refreshing recovery does in turn based, but it's great in RTwP. With the robe of the weyc and the singing scimitar, you can open every fight with two super strong invocations very fast, give yourself +3 power levels and apply brilliant to your entire party. Be sure to bring a priest to cast salvation of time, since the brilliant has a very short base duration.