Yes (assuming you've got Quicktime or other player software that can play m2ts files)
I'm my opinion, version 11 is one of the most stable and versatile versions of the entire program. Assuming your system is stable.
You can find my review under Details on the left side of this page.
"can process m2ts, mp4, typical smart phone video files, directly. (just put them in the timeline without converting them first)"
I do that. Projects get a "setting" to match the first clip you use. My projects are usually started with a .m2ts clip. I have tested mixing a .mp4 clip into a project and that went well. I have not personally tested the "Mobile Devices", but it is listed.
"Can burn to a folder with DVD and AVCHD formats for later copying to a DVD. Play DVD on DVD player with menus designed in PE 11"
I have done that.
"can produce or render a project to a m2ts file that I can execute by just double clicking it."
I have produced or "rendered" files that play on my computer. The output choices are many! Usually I pick a 1920x1080 .mp4 for playing on my computer. I pasted a screen shot so you can see how many output choices you have.
"What has the history been so far with PE 11? Does it Crash often? Does it require and patches or additional files?"
I have had no trouble at all in versions 9, 10 and now 11 on three different computers over the last 3 years. PrE is a mass market product. I have no idea how many are sold. The few that have computer problems show up here because it seems the easiest place to get advice. So, you can always read where someone is having trouble. The common problems stem from have an older or weaker computer, out of date drivers, not enough memory, etc.
I'm sure you know that .m2ts AVCHD video works a computer hard. One of the "features" of PrE11 is that it is the first version that fully supports AVCHD editing.
Version 11 released 9-25-12 http://forums.adobe.com/message/4725394
The USUAL schedule is once a year, in time for the holiday buying season
If you really have a link to Premiere Elements 12, please post it