The looked around the heavily Chinese-inspired museum.
1) Is a hyphen to be prefered here?
2) Is 'heavily' perfectly okay here?
anonymous 1) Is a hyphen to be prefered here? ) I guess you mean "they" looked around. (typo) The hyphen is necessary.
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anonymous1) Is a hyphen to be prefered here?
preferred (sp.)
I guess you mean "they" looked around. (typo)
The hyphen is necessary.
anonymous2) Is 'heavily' perfectly okay here?
Yes.