Glad to see this question here. :)
Our stats on Area 51 are good with the exception of questions received.
Needs Work – 10 questions per day on average is a healthy beta, 5 questions or fewer per day needs some work. A healthy site generates lots of good content to make sure users keep coming back.
With us at 3 questions per day, it makes it hard for newer users to establish rep. It's been discussed previously how we're sort of a low voting site. And trying to get votes by answering old questions is very difficult. A new user has a better chance of getting an up vote or two for a good answer to a fresh question. Plus, as noted above, it encourages all users to keep coming back.
I think it's a great idea to ask established users to ask more questions if they are willing. Drawing from my personal experience as a supervisor at work, it's always good to periodically do the thing you want other people to do to (a) demonstrate how it's done and (b) remember how really hard it is to do that thing so you'll be a little more sympathetic when others struggle to do it well! :p
For sure there is no need to seed the site with questions the OP doesn't care about. But with a little bit of thought, I generally find there is something I'd like to know a little more about, perhaps from a different tradition that I know little about. That gives someone else a chance to show their expertise and hopefully earn rep and the respect of the community. This is what I was doing with this question,
[Why is Budai often associated with the future Buddha Maitreya? although it might have been too tough of a question as even Wikipedia didn't have much. But who knows...maybe we have a Budai expert on staff somewhere just waiting to shine. And I really would like to know. :)
As far as promoting the site, I know SE questions are sometimes shared on Facebook. Would it be improper to share them specifically to a Buddhist group page on Facebook or Google+?
Also, remembering to vote is really key in demonstrating what IS a good question or answer and sometimes voting is so low; everything just blends together. Plus it doesn't help when people don't get positive feedback for their good efforts or the tangible reward of earning rep and privileges. Is there anything like a banner than can be added to the site to remind people to vote? It always surprises me when I see people posting in comments about what a good answer something is but there are no votes cast on it. Likewise with accepting answers sometimes.