There isn't really any way anyone can know if the other is being truthful and honest.
I asked a Domme one time as to how they could determine who is really being genuine on line.
She said that the ones who do everything they are told without any problems are the ones who are usually lying.
The ones who never seem to have difficulty with tasks, and say everything they think the Dominant wants.
That's not saying that all submissives who do this are lying, but most aren't being very truthful.
That being said, slave and submissive are just relative words, and it depends on what they mean to you personally.
I am submissive; I can also consider myself a slave as well. I don't think I have to give anyone a definate reason either, it's how I feel.
Yes you can successfully have an online relationship, but that depends on what you want out of it.
You definately cannot compare real life to online only because of the lack of physical interaction. If you can live without the physical and you can trust the other person, it's not impossible, it can work.
Being submissive is all about the mind and being online can enhance that submissive feeling. The only drawback is that basically you are doing everything on your own, and only have conversations with your Dominant.