1) In TLA, she rolled as an exile of the Northern Water Tribe, a young healer who used bloodbending to repel a fire nation attack & was subsequently banished for her blasphemous use of her people's traditions.

In LoK, she reincarnated as an acrobatic thief & trickster, getting by in Republic City by ripping off the ultra-wealthy & various crime bosses. She started with no bending but later became a bender following the events of the Harmonic Convergence.

2) Loma of the Water Tribe had a pretty fraught relationship with the Gaang, thinking them too soft for the war. She encountered them throughout their travels, joining for a time before her bloodbending came to light & they parted ways. Only years after the war concluded did she finally seek peace & go on to pioneer modern medicine.

Eko mostly spent her days evading the Republic City Police until her reputation for streetwise & chi-blocking saw Team Avatar knocking on her door for info about Amon. She jived with the team and joined up, bringing a puckish presence & intimate knowledge of the RC underground to the table.

3) Loma was a skilled combat bender, but was ultimately a far more gifted healer than a fighter. She learned to use bloodbending not as a weapon, but as a surgical tool, using it to staunch bleeding and rescue even the most grievously injured. (as well as developing the ability to assess and diagnose other conditions by way of reading the body with her bending.

Eko thought little of bending, taking advantage of the broader cultural underestimation of non-bender to flip, weave, and dodge her way around even the most skilled benders' abilities. She got knocked down hard when she tricked Vaatu into fusing with her instead of Unalaq, successfully arguing that the elder waterbender would try and use His power to create order and control, something antithetical to the Spirit of Chaos & Disorder. She tried to use it as a means of getting Vaatu back in the Tree of Time, but ended up permanently fused.