Not all of the ELA rebels were infected with the C-Virus, like the first one Ustanak kills. It is unknown whether Carla used one strain for all J'avo or if she made a variety using genes from different creatures rather than the Complete Mutation Species all being random. The ELA J'avo were under their group's orders. The Lanshiang and Neo Umbrella J'avo follow Carla's orders. She also recruited some of the Edonian rebels to essentially act as her security while she was in Edonia.
Carla was infected with the Enhanced C-Virus, same as Piers and Simmons.
All of the viruses in the series rewrite cells at the genetic level. Since all viruses have a limit to how many genes they can hold, it is unlikely that Carla created a single "master" strain containing so many animal genes, so she most likely created a variety corresponding to the genes they contained. Judging from the amount of J'avo, she had lots of samples in general so there's no reason she couldn't have a variety.
Lepotica itself did not exist before 2012. The C-Virus variant given to Nana was one of the byproducts of Project Ada. After the Marhawa School Incident, her tissue fragments were recovered by Carla and used to create an improved version which then led to the Lepotica. The Lepotica itself is still a byproduct of Project Ada, there's just a whole story to it.
Benford had to have a hole in his security detail to ensure he would be infected/killed, and Helena leaving her post was that hole. Holding Deborah hostage was to ensure Helena would leave her post. She feels guilty afterwards and returns, which is when she finds Zombie Benford and then Leon finds them.
All of the BSAA personnel died as both choppers blew up mid-air. What good would calling for backup while you're flying fast through the air?
Obviously The Family have more power and connections than Hunnigan can hide from. They wanted the plane as a whole to go down to ensure Leon and Helena died, including any potential witnesses.
Neo Umbrella was a secret underground organization that was not involved in many incidents until Edonia. Prior to that Carla still faithfully towards Simmons' orders and goals while secretly building her own organization using his gifts. Being his right hand, Carla knew how to hide her activities from Simmons and The Family. Having his total trust helped.
Simmons initially tries to convince Sherry of his views, he then orders them all disposed of when she refuses. He and his men were distracted by the situation in front of them, so didn't see the J'avo. He fell on to the train in order to simply escape.
Rebecca calls Chris out on not wearing bio-protective gear in Vendetta and he just says "Yeah, well." The truth of the matter is that some of the appeal of these games and characters is in the appearance of the characters, that appeal goes away if you cover them all up head-to-toe. In the plot it can be explained by the characters being focused on rapid-response or emergency situations.
We don't know what kind of further research Carla was planning because she died.
Any modified Progenitor Virus developed under the t-Virus Project is officially classified as a t-Virus. The terms "Progenitor Virus" and "t-Virus" are sometimes used interchangeably by Umbrella pre-1998 since it was still in development. t-Veronica is a modified Progenitor strain developed as part of the t-Virus Project so it is classified as a t-Virus. She just gave it its own name. There was no "t-Veronica Project", as Alexia was simply conducting her father's t-Virus Project.