I am very confused
It might be they are saying the same thing since your home page is meta refreshed to an inner page.
1.) Is the meta refresh timed or is it a 0 second delay before the redirect?
I have not tested it myself , because if I redirect it's using a server-side method, but I've read Google treats 0 second meta refreshes similar to 301s, but not if the time to redirect is greater than 0. I don't remember exactly which thread, but if you search around in the old threads here (think 3 or more years ago) you should find what I was reading. It's one of those things that sort of stuck with me from a long time ago, so I'll not be citing my sources on this one, but I know it's 'here somewhere' for you to find if you want.
i also like to mention that Google might be shrinking the PR of the sites who are redirecting their pages.
2.) Links passed through redirects do lose PageRank.
There's a very recent thread here with a link to an article about it, and, yes, links through redirects do pass less weight than those linked directly.
Personally, I think you're taking it a bit further by using a meta refresh, because what I read 3 years or so ago may not still be the case today, and IMO you are taking a much greater chance of nothing being passed using the meta refresh rather than a proper redirect.
3.) The type refresh will not in any way affect the PR of the /blog page other than to possibly not pass the weight of links to http://example.com/ to it.
What I mean is the PR of /blog from the pages linking directly there, rather than to http://example.com/ will not be discounted because of the use of the redirect. So, the link weight from the home page may not be passed there, but the link weight it was itself from inbound links directly to it will not be discounted.
4.) The ToolBar PageRank is out of date by the time you actually see it (unless they've changed the publication process and I've missed it), and an estimate, so it could be, if you put the 'refresh redirect' in recently and it's 0 seconds and it passed weight it may not have been in place on the day the new PR value for the ToolBar was estimated, hence the 1 you see and will see for the next 3 months or so regardless of any changes you make, even if you redirect the root (http://example.com/) with a 301 which is known to transfer a high percentage of link weight... IOW: Your PR will be updated internally by Google within their system, but you won't see any change, except possibly in your rankings for about another 3 months.
5.) Can I ask why you would redirect to /page?
We actually had a recent discussion here about that too, and I'm more curious than anything... Some others here do it. I've seen it done before. I personally don't like it, but if that's where it's going to stay and you don't ever plan to use http://example.com/ as a live URL then I'd recommend you properly redirect it using a 301 and a server-side language.
If you are planning to some day use http://example.com/ then my personal preference and recommendation is to place a single keyword rich link on the 'home page' (domain root http://example.com/) so people can visit if they feel like and link to /blog from there. (Note: Do NOT link back there from /blog or anywhere else. Only link to /blog from there.)
EG http://example.com/ would say:
Welcome to Example.Com
<a href="/blog">Wigets and Widgeting Instruction Blog</a>
Option number 3 is: if you plan to use the http://example.com/ location again, use a server-side redirect and a 307 status code and see what happens... I'm not sure on this, because a 307 is temporary and this is the right situation to use one, and I have used them successfully in temporary situation, but it was not for an extended period of time and this is more of a 'try it and find out' thought than the other ideas.
6.) Why is neither page ranking? In my experience, search engines don't always handle 'home page' to 'inner page' moves the way we think they should. I have not personally redirected a home page to an inner page, but there are those who do using a server-side language and it's worked for them, so it's possible, but... The way you are doing it could be confusing, and if there is a delay in the redirect then IMO it will not only not work, it will not remove the home page from the index, so what could be happening is the search engines are not treating your meta refresh as a redirect (for whatever reason) and your link weight is 'split' between the root http://example.com/ and the page you have been building links to /blog.
The reason I say they don't always treat 'home page' to 'inner page' moves exactly as we think they should is I had a site which was completely about a single topic (about 5 pages) and I built another site with expanded topics and the contents of the site became a sub-topic on the new site... I redirected the old site to the correct directory on the new site. The old site had a DMOZ and Yahoo! directory listing at the time, so I wanted to preserve the link weight and take visitors to the correct location. Yahoo! listed the old domain until the day I let it expire and quit redirecting it, and Google listed the new page on the new domain for quite a while and then dropped it. The DMOZ link was changed and the Yahoo! directory link was removed, so I let the domain expire and within a couple of days of the redirect being removed the new site ranked much better... Anyway, not exactly the situation you're talking about, but whe you do things a bit different than other people it can sometimes not work out the way you think it should.
There are times I might take some 'calculated risks' but redirecting a 'home page' to an 'inner page' with a meta refresh is not one of them. I would use a proper redirect status code, and server-side scripting language to do it.
I'm not sure if I answered all your questions, but a bigger concern I would have over the PageRank you see (especially since it won't change in the ToolBar for about another 3 months) is why is the page not ranking? If you find the answer to 'why is it not ranking' my guess is you'll be happier with the number you see at the time of the next PR update...