1. After successful boot, I've noticed, that buttons above the
touchpad[1] stopped working. Tried to debug the thing, but they do
nothing even under xev or in showkey - seems like they dead. Didn't find
anything interesting by searching the net.

Longshot (since i've had one instance in the last few years where i need to rebuild xorg after a kernel update) have you tried rebuilding the xf86-input-* packages against the new kernel?

2. This one is more annoying. After boot to the new shiny 4.x kernel,
devices connected via the usb seems to have aggressive power safe mode.
For example - if I typing for a while everything is fine, if I stop for
a couple of seconds, and then start to type, for approximately 2 seconds
there is no response from the device, and after that i can type again.
Note, that during those 2s no buffering is done, so whatever I'm typing
in this short period, is lost. Same goes to the mouse movement and
buttons.

I haven't had much luck with USB power saving working in a useful way and leave it off. Strange its been enabled by default for you.

cat /sys/bus/usb/devices/*/power/control will show you what the current settings are.

The options are on/auto.

"on" means that the device should be resumed and autosuspend is not allowed.

so that's what you want. It can blanket set with;

echo on | tee /sys/bus/usb/devices/*/power/control

Or you could work out which devices are actually a problem and just "on" those particular ones.