Puck.IR() definition clarification needed

nRF Connect and nRF Toolbox did connect to Puck only for 10 secs and disconnect somehow

It might be worth trying to change the battery in your Puck? A nearly flat battery can cause problems sometimes.

If firmware can bring better results I will give one more "harder" try :-)

Actually from the changelog it looks like 1v92 had the 'higher power' output already - but you get loads of extra features in 1v94 anyway :) http://www.espruino.com/ChangeLog

2) In case I have to use transistor (1 input leg only), should I use 2 transistors ?

Yes - you'd need one NPN and one PNP - and the resistors for them. Honestly I'd just use the TLP240D linked above - it's a really nice easy little component to use (and won't require resistors/etc since the LED can take as much power as the nRF52 can supply). It's also totally isolated, so you can use a bigger battery for the IR LED if you need to.