There's two aspects here.
For one, in many countries, especially the US, you're required to disclose the inventor truthfully. Not doing that could suffice to invalidate the patent or you could sue for it to be transferred to you, etc, depending on location.
But let's put that aside as it's a lot of work and proving etc.
The subject matter of a patent application (=what you're trying to patent) needs to be novel and non-obvious. That means, compared to all publications out there, you need to claim something unknown and not obviously derivable if you want your application to get granted.
But, the decision, while it should be, is not completly objective or perfect (of course not). It's made by a patent examiner. If that patent examiner doesn't know about yor mails and your blog, they don't know they shouldn't grant the patent application.
The resulting patent would still be invalidatable with proof of your public disclosures (sending it to a few companys without making them keep it secret counts as public disclosure). But at first, it would be a granted patent.
So, yes, technically they could or could try, but no they couldn't as in it woudn't be a valid patent.
Btw. almost the same goes for yourself. The US offers a grace period for disclosures by the/an inventor where you can still file a patent application and get it granted afterwards, but for most parts of the world your "I haven't patented it yet." is a terminal "I never will be able to."
Some countries like the US offer a grace period for publications from the/an inventor that allow the inventors to apply for a patent even after publishing the invention. Only in those countries it is possible to get a patent after a publication. A non exhaustive list: http://mewburn.com/resource/grace-periods-for-disclosure-of-an-invention-before-applying-for-a-patent/
In the US that's 12 months after the first publication.
There are also grace periods for utility models, in Germany that would be 6 months for example. That might be a way to get at least some protection (10yrs).