Hi,
About a half domestic companies are unwilling to employ ‘old’ people and place a limitation on qualifications by gender.
1. a half domestic companies / half domestic companies.
Which is right? You need to speak of 'half of domestic companies'. The article 'a' can be used, but more commonly I hear 'One half of . . .' or simply 'half of . . .'
In business-oriented writing, people will often say '50% of . . .'
2. I don't know if 'place a limitation on qualifications by gender' is appropriate expression. No, your meaning is not clear.
I want to express that when companies hire workers, they impose different requirements according to the applicants' sex. <<< This is a much better way to say it.
About 50% of domestic companies are unwilling to employ 'old' people, and impose different requirements according to the applicants' gender.
The comma is to show that the scope of 'unwilling to' does not extend to 'impose'.
Best wishes, Clive