how Eren came to be a Titan.

I think that the Titans were a result of some plot against humanity that went horribly wrong. Perhaps humans originally created Titans long ago by injecting humans with Titan blood? This would give us a reason as to why syringes keep being shown throughout the series, as well as a possible inclination as to what exactly Dr. Jaeger has been up to. This could explain Eren's transformation into a Titan as well. Perhaps Dr. Jaeger injected him with Titan blood before he left. Just a speculation.

I think that the ability for humans to transform into Titans has been around since the beginning of the Titans. I also believe that human/Titans are able to crystallize themselves to prevent aging. This may be what Annie is doing when she covers herself in crystal after being captured. It may also be an explanation for the development of the Armored and Colossal Titans over Eren - Eren is much weaker and less developed than they are. This is because, in my opinion, Ymir is from a much older generation of Titans, Reiner and Bert are from a generation younger than her, and Eren is from the youngest generation. Why do I think that Ymir is from an older generation? Because of this:

http://www.mangahere.com/manga/shingeki_no_kyojin/c018.5/10.html
http://www.mangahere.com/manga/shingeki_no_kyojin/c018.5/11.html

The Titan refers to Ymir as "Ymir-sama (Lady Ymir)" and believes that the girl is one of her people. This could be because this is the first time the Titan has ever seen a human, and it knows that Ymir has the ability to turn into a human. Now, we do not know for certain if this Titan is referring to the same Ymir, but this can't just be a coincidence. Obviously if this is the same Ymir, it would mean that she is of some sort of nobility or reverence among the Titans. Keep in mind that this side story took place in the past. Ymir also had the ability to turn into a Titan when Reiner and Bert were children, so there's no telling when she attained this ability. She may have even been born with it.

I believe that all Titans were once humans, but some of them have lost their human senses over time and have become more Titan-like, or completely overcome by their Titan halves.

he obviously has the ability to create unintelligent Titans from humans.

I think he might be Eren's Dad. I have a theory that he started losing his mind after spending too much time in his Titan form, like it has its own will kind of thing. Which is why he was so desperate for Eren to go back and learn about the Titans and become a Titan himself. I'm just speculating though.

Regains the use of his body again after he injured it owning Annie. I can see him dying though, going out like slaughtering a ridiculous number of Titans on his own to save people.

I dunno, Eren was able to fight the Armoured Titan fairly well, he got a bit of a resolve powerup but still, probably would have won if the Collosal didn't interfere. He'll probably get something at some point I guess.

I had actually dismissed that idea at first because of how he acted toward the scout he saw when he was first introduced. He seemed to act as though he wasn't sure if the humans spoke English and asked what the maneuvering gear was. Surely Eren's father would know those things. There was one other thing he said that made me dismiss that point, but I can't remember at the moment. With what you said about him going insane and becoming a Titan himself, though, I guess that could make a little more sense, but I'm still holding some suspicions.