Alright, here it is. The ultimate, end all be all explanation of ALL the timelines created during the Android/Cell Arc, written in a way that is easy to understand and avoids paradoxes and plot holes.
1st Timeline (The Original): Trunks¹ used the time machine to create a 2nd Timeline, where he warned the Z-Fighters of the upcoming Android threat and where he obtained blueprints to create the remote to deactivate the Androids. However, Cell¹ would kill him and steal the time machine to travel even further into the past, creating the 3rd Timeline.
When Cell travels, he goes to the
same altered Timeline that
Trunks created. Meaning no new branching path was created for the Third Timeline, and instead it would be a branch off the already branched out timeline. (Though given this is never indicated, this is mere speculation, and it's more likely none was created, given the amount of Time Rings signified in Super.)
2nd Timeline (Unseen): This is where Trunks¹ went in his trip to the past. This timeline is almost identical to the main one we follow in the show, with the only difference being that no version of Cell came from the future here. How the events played out here is mostly unknown. On Gero's lab, Cell² is being incubated but his fate is also unknown.
Unsure. Cell goes to the same Timeline Trunks came from (he says it was pre-programmed to do so for him, all he had to do was alter the year) so if anything the Unseen Timeline is where Cell went to, which would then be our Timeline. Of course, there IS an Unseen Timeline, because that's where Trunks went to get the means to kill the Androids', but it likely exists nebulously branched, because as far as we know they traveled to the same timeline due to the Time Machine's programming. Essentially, a mini-plot hole.
3rd Timeline (History of Trunks): This is where Cell¹ went in his trip to the past. Here, he buried himself underground for four years, waiting for the Androids to be unleashed. The Androids from this timeline would kill the Z-Fighters (including Piccolo) just like in the original timeline. Then, Cell¹ would try to absorb them but he underestimated their strength and ended up killed (he can't sense their power levels).
Many years later, Trunks² would travel to the past, creating the 4th Timeline where he would obtain knowledge of Cell. This would allow him to stop Cell³ from stealing the time machine again.
This is incorrect. Any Cell seen or described originates from the same Timeline a given Trunks is from, waking up after Trunks' victory. This specific fact is why when Trunks returns to his original Timeline, Cell is there to be killed by Trunks, as you yourself have noted. However, Cell notes within the story he went back in the first place because the Androids
were killed. This means that what happened is Trunks ganked the 'Droids, prepared to return home, and got ambushed by Cell (Which you have listed as Timeline 1). This then allowed him to travel to the Timeline Trunks had previously locked onto, where Trunks found out. When he returned home, he ganked that same Cell (earlier in his own personal Timeline). Also, History of Trunks is merely the prequel to our Trunks appearing in the main story, so it moves continously from HoT to Main Canon events, meaning it cannot be separated in this way.
4th Timeline (Main One): This is where Trunks² went in his trip to the past. Cell¹ was already buried underground in the 3rd Timeline (the one where this timeline branches off) so he was duplicated the moment Trunks² arrived here, creating Cell⁴. Piccolo wasn't killed in this timeline so he would fuse with Kami to become stronger. This new "Kamiccolo" would be a major obstacle for Cell⁴, who would resort to absorb humans in Gingertown to become stronger than him. Krillin would kill Cell⁵, who was incubating in Gero's lab. Cell⁴ would absorb A17 and A18, becoming perfect. Gohan would kill Cell⁴ and Trunks² would return to his time with knowledge of Cell.
In conclusion, we end up with 4 timelines, 5 Cells and 2 Future Trunks.
This is correct. Once Trunks went into the past, Cell was already there due to going to a time period earlier within that same Branch. Yes, there are two Trunks, because the initial one we see dies due to Cell, and the events play out as we see on screen. The only confusion would be how they both return to the exact same timeline and create the Unseen Timeline.