No need for a visa, as the UK is a participant in the Visa Waiver Program.
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.
yes
no