Is it permissible to receive another suitor after giving preliminary approval to see a previous one, and does the Hadith "None of you should propose marriage when another has already done so" apply to this situation?

There is no harm in receiving the second woman who wants to propose to you for her son, as long as you have not agreed to the first suitor. This is not considered proposing over an existing proposal, which is forbidden. Rather, proposing becomes forbidden only if you have already accepted the first suitor.