Did you know your friend was suicidal? I don't see anything in those text messages that would indicate that so how could you know? People don't answer cell phones or texts for a number of reasons--having the phone off or charging or just having left the thing at home are very common reasons. No one on earth would read anything into that.
One thing people do when someone is in a great deal of pain from the guilt they feel when something bad happens is to say you're not at fault. It's like the worst thing you can do is own up to something. If you're guilty, it's far more emotionally and mentally stable to own up to it, but then you realize you didn't do it intentionally or to be mean. Then you resolve yourself to not do that thing again.
In this case, I'd side with people who say you're not at fault here. I don't see that at all. Did you have any idea this person was so emotionally vulnerable that not responding to a text or two would push them over the edge? Of course not. Some people are just so close to the edge that a light breeze or a banana peel is enough to push them over. What that means is that whatever was going horribly horribly wrong in their life had nothing at all to do with you and was well in the works probably long before the two of you even met.
I just don't see negligence here, and I'm not all about validating others who desperately need to be told that's "not your fault." Here, that is truly the case. I am sorry for your loss.