1. Not really. There's some value in DWing if you're in a game with a huge number of magical item drops, but the big problems are:
1A. Even warcaster doesn't get around the whole 'how are you accessing your material components' question unless you're using a staff -- and there's no way to get a DEX staff without multiclassing.
2A. It just doesn't do that much damage unless sexed up. The old Nadrigol guide recommended taking a level of Fighter for +DEX, but I find that arrangement foolhardy. But until you get to level 14 and/or use Tenser's Transformation, you do all that rigmarole for... what? An extra d6 damage? Compared to using, say, a rapier for your attacks, you do an extra 1.5 damage a round when you're not hasted and a mere .5 damage when you are.
Even if you are okay with that kind of ruthless prioritizing, it'll usually end up even less than that because of bonus action clog and the limitations on drawing weapons. When you want to use your bonus action for something else (like, say, a Misty Step or to start your Bladesong) you end up losing out on damage because you're using two shortswords instead of a rapier. For example, say you're a level 8 or so Bladesinger. You get involved with an 'Easy' combat, one that doesn't tax your resources too much. You budget two Shields and a Misty Step (a trivial expenditure of your resources) and just wail on the foes with your blades.
ROUND 1
16 DEX Rapier BS: Bonus Action for Bladesong, runs up and hits the foe twice using extra attack. 2d8+6, average 15 damage.
16 DEX Shortsword BS: Bonus Action for Bladesong, runs up and hits foe twice using extra attack. 2d6+6, average 13 damage.
ROUND 2
16 DEX Rapier BS: Hits the foe twice using extra attack. No bonus action. 2d8+6, average 15 damage. 30 DPR total.
16 DEX Shortsword BS: Hits the foe twice using extra attack, uses bonus action for a shortsword attack. 3d6+6, average 16.5 damage. 29.5 DPR Total.
ROUND 3
Rapier Elf: Two more attacks. Uses bonus action for Misty Step. 45 DPR total.
Shortsword Elf: Two more attacks. Uses bonus action for Misty Step. 42.5 DPR total.
ROUND 4
Rapier Elf: Two more attacks. Hanging bonus action. 60. DPR total.
Shortsword Elf: Two more attacks. Uses bonus action for shortsword attack. 59 DPR total.
So really, it's often a DPR increase when you count the opportunity cost of bonus action clog. It's too much rigmarole for little benefit.
DWing can be worth it in the late game in certain circumstances (You have poisons, a lot of magical items, Song of Victory, a Tenser's Transformation or two), but it's generally not worth it. It's especially not worth sinking permanent character resources (like that Dual Wielder feat) into it.
2. I have a Tressym familiar, which has a bunch of great goodies, including seeing Invisible creatures. The problem is if it dies, I don't get another one. I really love cats RL and the thing is totally adorable, so I find the minor increase in power at higher levels not really worth risking my familiar from a roleplay standpoint. I also have a Ring of Spell Storing, however, so my plan right now is to use my Familiar as an extra concentration slot and have it stay out of danger areas after using the spell on me.
3. Sure.
For Easy/Medium encounters, I generally use spells like Protection from Good and Evil/Blur to conserve spell slots.
For Hard/Deadly encounters with solo or one or two heavy-hitting monsters, I use Ray of Enfeeblement or Telekinesis, depending on if they're a STR-based attacker or not.
If I want to drain an monster's Legendary saving throws, Ray of Enfeeblement and Sunbeam are quite efficient at doing so, but my party is generally so efficient that they can kill the target with melee damage faster than making an opening for a save.
If the game is foolish enough to throw a bunch of ground-based melee opponents at you, upcast a Fly for the party members that are juicier targets. The barbarian and STR-based Eldritch Knight may balk at having to plink away with javelins, but expending no resources other than a level 5-6 spell is a good use of a spell slot.
If you're fighting a lot of threatening CR 2-6 mobs, "deal with them later" spells like Banishment, Wall of Force, and Fear have your back.
If you're unsure of what to do, it's rarely a bad idea to throw out Web, Phantasmal Force, Suggestion. You can also run around with a Conjure Elemental, though keep in mind that unless you have a Banishment or Dispel Magic on standby you can't really use your concentration slot to do something else. It's metagaming, but I like to start the day out on canned adventures or blind dungeon crawls with a Conjure Elemental because it's a good use of a concentration slot but you generally have the option to switch over to something better later in the day.
I haven't tried this in actual play yet, but for mass encounters I definitely want to try out Transmute Rock + a good concentration spell like Sleet Storm or Black Tentacles or Watery Sphere.