I will be spending cca 8-9 hours at Heathrow during the night, is there a free wireless internet somewhere? Or any other suggestions on what to do? Thanks

I stayed at that airport for a long stop over. I didn't find any free wireless internet but there were a lot of computers you could use for a fee. There's always duty free stores to kill time and and there's cafes that have great breakfasts.

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<hr>There's always duty free stores to kill time <hr></blockquote>
Airside is closed at night so you can't stay there let alone shop there
For OP see sleepinginairports

There are some airline lounges with free wifi, but you normally need to get password from reception to be able to log on, and unless you are entitled to use the lounge, they won't give it to you.