I've tried dpkg -i command before and it did not work, however, this time it seems it worked (fasterN9 can be seen on the application list in settings). The output is quite extensive, I've copied only the last part of it:

https://www.dropbox.com/s/mtgsqqpy0q...2_10-18-02.png

There're messages concerning gpsmefoo app, that I've tried to install as a benchmark if installation process works after a couple of reboots.
Also, my dropbox does not have a public folder. I'll skip the screenshot, but I think I might have deleted it or something like that. Anyhow, when I manage to get it back, I'll start uploading pictures correctly.

EDIT: also, I still get an error when trying to install anything else, damn it