Is sharing research progress and ideas on blog acceptable?
Blogging is very common and appreciated in mathematics. For example, here are some blogs maintained by well-known mathematicians: Terry Tao, Quomodocumque, Tim Gowers. None of these blogs are devoted exclusively to mathematics, although each of them contains plenty of math. Each of these links to tons of other math blogs, so you can see many more examples.

I think that what you propose is a very good idea, subject to some caution. As Alexandros suggests, I would only discuss other people's ideas if you get their permission. (Or, perhaps, if you are discussing something publicly available. In mathematics this is certainly considered okay but you should check with someone in your discipline.)

Most importantly, I would suggest waiting to blog about your work until after you have completed it and made your results publicly available. (In math it is typical to post a preprint to the arXiv at approximately the same time that you submit your paper for publication, and at this point your work is considered public. But in some disciplines a paper is not considered "public" until it is formally published.) There are several reasons for doing this. One is that you avoid the risk of being scooped. Another is that, by waiting, you get to advertise your finished work. Typically, math blogs contain links to PDF copies of the papers they discuss. When I get interested, I often want to click through and read the paper!