Some unassorted thoughts: I use my operator/drifter only as utility. Self revives, crossing great distances, reviving teammates. When I used Zenurik I'd also switch to use the energy regen ability, but these days I use Madurai in order to be able to self revive on higher levels. Also Void Angels.

I have built some amps, mainly for levelling. 777 got recommended to me at some point and it works well enough so I've stuck to it.
I use the tether and heal teammates on invis arcanes on my operator. As well as two damage ones on my amp. Most of them aren't maxed.

I have maxed out Naramon, Zenurik, and Madurai and have all waybounds.
Way back when operators were first introduced I liked Naramon because I used a lot of melee. Then switched to Zenurik for the energy regen. Only (relatively) recently switched to Madurai, though I might have done so earlier had I been actively playing these last few years.

I want to like operator mode. I like the idea of switching out of your Warframe and just running around as a (mostly) regular dude. But none of the amps I've used feel great to shoot, the movement animations all feel awkward, and the operator is just fairly weak. I avoid Duviri whenever I can for the same reason. It just feels clunky and awkward and not good.

Also I use the drifter. Part of the reason being the operator voice lines which have become grating over the years. "tHe GriNeEr DeTeRiOrAtE oVeR TiMe, iS tHaT wHaT mAkEs ThEm AnGrY?!?!?"

To answer my own... well at this point survey:

• Yes, I do. Quite a bit actually.

  • I greatly prefer the Drifter.

• A decent amount, I'd say. A bit of research and a bit of grinding.

  • Yes, I have several and know of a few more I could build and might like.

• Yes, both types and I find them somewhat necessary.

  • Magus Replenish & Emergence Renewed on Drifter, Eternal Eradicate & Virtuos Strike on Amp.
  • Yes, all of them.

• I main Madurai

  • Yes, it is.
  • I've unlocked everything in the school and two 'represent' cosmetics.

• Yes, all of them.

  • Yes, I've unbound everything.

• Farming Thrax and Void Angels on Cascade

  • No. It's a high-intensity grind that I've never encountered someone else willing to do. In short: it's pure pain.

• Notably less effective but still useful.

  • Sometimes significantly more effective and always useful.

• Yes, Void Sling. I can't keep up with most other Tenno's bullet jumping but VS gives me an effective alternative to not be left behind.

• I like it, I find that it has great utility that supplements every Warframe pretty well.

• I love School synergies. So I don't use my Drifter as a "warrior" per se, but I do actively use School abilities. I typically run Vazarin, and the Void Snare mass-finishers are great for proccing Trickery and stacking Crescendo. Void Snare with the Phahd scaffold is exceedingly powerful. Drifter mode offers good mobility if I'm on Ivara.
• I have an Arcane Adapter-fitted 777 and 547. I plan to go through and make XX7s to get a feel for the other Scaffolds, but Phahd seems to generally be the best for Last Gasp recoveries.
• I use Magus Lockdown and Magus Melt for general use (Lockdown covers CC and demolysts; Melt covers Void Angels and Thrax). My 547 is fitted with... something. Whatever the standard became when the Zariman amp arcanes dropped.
• I almost always use Vaz. I started with Naramon. Vaz is, imo, the best general purpose school as it gives you free emergency invulnerability and lets you easily stack Crescendo. I use Madurai on Gyre and my health tank Sevagoth so I can lock in +125% power strength on their abilities. All my schools are maxed, and I have fully finished collecting all the Represent swag.
• I did most of my focus farm before Zariman, so my main methods of focus farming were fitting different nuke frames with Eidolon Lenses and farming ESO. When I managed to catch tricap groups with the alliance, I would use shards. I mostly did not enjoy the Sanctuary farm, as it was very repetitive and one-dimensional, but some methods were fun (like Nezha with the Akarius). Nowadays I could quite happily do it on Gyre or Sevagoth as they have very mobile nuking styles.
• Phahd spam is powerful, but it pales in comparison to the kinds of chaining beam incarnons we have now, like Torid and Boar. Void Snare spam is theoretically very powerful for objective defense, but I play Warframe for the movement, so it's not very fun.
• Everything about Vazarin is incredible.
• It's effective, but "maining" Drifter/Operator seems to run contrary to what makes Warframe compelling and unique. Drifter/Operator feels best to me as a component of your loadout.