yes
No need for a visa, as the UK is a participant in the Visa Waiver Program.
No, there is no need to have visa traveling to EU countries. But in countries like Russia, Ukraine, Belarus British may need some additional permissions.
Yes
not for a holiday
yes
No, they are European citizens.
Yes the man from China will need a visa to visit the U.K.
Yes
No, Serbian citizens doesn't need visa for Schengen countries, but they need visa for UK and Ireland.
She would need a UK work visa.
No. Since both UK and Czech Republic are EU members you do not need visa.