You seem to have missed a critical part of sneak attack, and you seem to not understand the mechanics of grappling in much detail.
I'll deal with Sneak Attack first. I DM for a group that includes a rogue. He has been able to sneak attack about 95 % of his turns in combat so far, for one simple reason: the group has a tank that stands next to the enemies. The important part of Sneak Attack is as follows:
You don't need advantage on the attack roll if another enemy of the target is within 5 feet of it, that enemy isn't incapacitated, and you don't have disadvantage on the attack roll
If your group has a tank, they are most likely going to stand next to the enemies. Just make sure you're attacking the enemies next to your tank, and you sneak attacks are going to be available pretty much every turn.
Now, on to grappling.
Grappling can never activate sneak attack, since they are special melee attacks, not special melee weapon attacks. Grappling replaces one of your normal attacks when you initiate the grapple. Once you have grappled the enemy, you don't have to commit anything on your turn to keep the grapple going. There are two ways a grapple can end: If you intentionally let go of the target, or if they try to break free. The first option requires that you actually say that you let go of the enemy. The second option forces you to do an opposed athletics check, but on their turn, using their action. Once you have grappled your target, you can use your action on subsequent turns to attack them. If you have the grappler feat, or if an ally is within 5 feet of the enemy (likely the tank of your group, if you do a bit of team coordination), you will be able to sneak attack them.
Your build seems to be trying to solve a problem that, for the most part, doesn't exist if you play in a group. Simply coordinating with your tank so you're attacking enemies within 5 feet of them will activate your sneak attack every time, unless you have disadvantage. Rogues in 5e are balanced around being able to sneak attack pretty much every turn. If they can't, they fall behind on damage compared to even the most tank-focused of fighters.
No, because the two conditions do not encompass every possibility.
If the Swashbuckler (S) has interposed himself between an Ally (A) and an Opponent (O). Each occupies a single five by five square.
Such as:
ASO
In this scenario, an ally is within 5 feet from the swashbuckler, but there isn't an ally within 5 feet of the opponent. Lacking an additional effect that will provide advantage to the Swashbuckler, Sneak Attack won't be available.
Similarly, if the Swashbuckler (S) is facing two Opponents (O and X), there are several configurations in which Sneak Attack isn't available.
To summarize, the following conditions will prohibit you from using Sneak Attack, assuming there isn't an external effect providing Advantage.
- Swashbuckler is within 5 feet of more than one hostile creature or character.
- Swashbuckler is attacking the target at melee range and a friendly character or creature is within 5 feet of him but isn't within 5 feet of the target.
Per a twitter post by Jeremy Crawford, Rules as Intended want the Swashbuckler to be within 5 feet of the target. In effect, Rackish Audacity should be written with "except" instead of "other."
Best Answer
to answer your questions in order.
Yes. Weapon of the Gods will work extremely well with your rogue powers. It will even add the radiant keyword to them. This is especially useful when dealing with undead. Your weapon remains a light blade/crossbow/short bow so you can definitely continue to inflict sneak attack damage.
Yes. The status affects inflicted do not conflict with the damage type. In fact the damage type is added to the damage type on the power (for instance if the power deals necrotic, it would also deal radiant).
Yes. The full version (not hybrid) of sneak attack requires you to hit with a specified weapon, not that it be a rogue power, so cleric powers are great (provided your valid rogue weapon is the implement or the weapon for the power). To add to this, the hybrid version of sneak attack (labeled "Sneak Attack (Hybrid)") does require you to use it with rogue powers and would not work in this case.
So yes, your planned build works just fine with the main class as rogue and a multi-class to cleric taking a cleric PP works just fine.