Clan wars can only be started by higher ranking members, though I honestly don't know the details. There's a thread somewhere out there that explains it all, but I haven't been interested enough to go looking for it. As for the whole regular member thing, it's more of a formality that shows that you are a trusted member of [elite] as opposed to all the questionable new recruits. Eventually you can become a veteran member and higher, which gives you more and more power and responsibility.

Also yes, your vote does count a lot more as a regular member as opposed to a probationary member.