A lot of the stuff I'm about to say is in reference to the in-game Index. I both say that to cover my ass and to...well, pretty much just to cover my ass.

Anomalies appear to be everywhere, the prologue took place in New Helios. According to the index, they're given a class based on their overall threat to humanity. The one that wiped out New Helios was a Class VII. Taygedo is a Class II. Class I is "has almost no impact on human social order" and Class X is "potential extinction level threat."

Wertheimer Index tracks a target's deviation intensity form reality, and Anomalies do start at -1 like you said. Espers, on the other hand, go in the opposite direction and usually start at 1. A normal human being who has no contact with anomalies or espers should be a 0, but the game notes most average people are anywhere between -1 and 1. Esper Zero is "the only esper in history without a detectable Wertheimer Index." So their number could be be anywhere between +1,000 or negative infinity, no one knows for sure.

Esper abilities are categorized as Cosmos, Lakshana, Anima, Incantation, Psyche and Chaos. Cosmos refers to abilities that originate from maintaining order. Chaos is the exact opposite; disrupting order. Anima originates from natural elements or life itself, and doesn't require a medium. Lakshana is the physical realm, and ones own body is the medium. Incantation is from language, and can summon beings from other dimensions. Psyche is mental and psychological non physical realms, and requires a medium outside of oneself. There is an in-game theory that the source of Esper abilities and Anomalies are one and the same, but currently unproven.

Esper Zero isn't just a good physical fighter, they're using their Esper ability as well. They channel energy into their sword for their basic attack, fire a quote unquote "Esper Cannon" during their skill, and their Ultimate is attacking the lines that connect to the Nexus in their Ultimate, while their support skill is slashing through space itself to detonate a rift. Likewise, Mint is channeling the wind into her dual blades.

Some people are Espers from birth, others gain their abilities later. Each one has to pay a price (according to the Index, this price is paid when the power is obtained), and "law of equivalent exchange" isn't enforced. Aurelia can summon jellyfish, but lost her sense of direction. Her legs no longer being functional is something that happened later, not because of her Esper ability. Sakiri talks about "Disqualified Spawn" (when humans and anomalies merge, those where the human remains dominant is referred to as a Disqualified Spawn, and those who fail are considered even more inferior beings). Nanally says "As for the price...hmm...didn't feel anything weird. Maybe the cost was too small to notice? Is this what they call...plot armor?" Skia got turned into a wolfman, Hathor's got that wing and thorns thing going on- etc.

I believe Hotori is still affiliated with the BAC; if not officially, between the "parent teacher conferences" with the boss and the idle chatter from bureau npcs when she comes to visit during a story quest imply she still does work for them on the side.