After this recent update Version 53.0.2785.143, Bookmarks are removed.
Edit: It would seem the "GoogleChromePortable\GoogleChromePortable.exe" opens in a different view to opening "GoogleChromePortable\App\Chrome-bin\chrome.exe" directly. My shortcuts I have created differ from opening within the PA app.
Edit2: Subsequent to this update, I am noticing erroneous tabs opening for http://www.benimicinode.com/. This has no nearing on my current browsing habits or anything malicious on my own workstation. I run my workstation lean and clean. Install this with caution.
Regarding your first edit - That is correct, setting shortcuts bypasses the portability code we've set. IF you wish to use shortcuts on a single machine, we reccomend installing the local version of Chrome rather than the portable version.
Regarding your second edit - This is not anything to do with the portable package nor Chrome itself, both are scanned as clean prior to release. IT sounds as though you may have picked up a virus inadvertently. I reccomend doing a virus check on your machine.
In addition to our own code being scanned, it's worth noting that everything that's ours in that package is open source with the source code included and that Chrome is downloaded from Google itself as you install. If you're seeing random tabs open, your PC is infected with something. Or your local network is.
It's also possible you're browsing sites showing infected ads. Even Google AdSense has issues with this so you'll occasionally see full screen ads claiming you're infected pop up on PortableApps.com, reddit, imgur, etc, all of which use AdSense.
Sometimes, the impossible can become possible, if you're awesome!
re: Edit 2 - I had the same problem - my chrome browser, on startup, opening a tab to benimicinode.com (and redirecting to yet another site). It turned out to be a fake malware version of the Adblock Plus extension.