How are primary monoclonal antibodies for screening mutant cells made, physically?
Monoclonal antibodies are typically manufactured from a hybridoma cell line. If you are able to obtain hybridomas already made for your antibody (not very likely), or another antibody against your protein, then it's quite easy to produce the antibody yourself. The hybridomas secrete the antibodies into the media, so after growing a bunch of cells, you can purify the antibody from the media with a protein G column. 

However, there are not very many hybridoma cell lines available. It's a lengthy and expensive process to make your own (several months and thousands of dollars), even with the help of a core facility/company. You would provide the facility with several milligrams of your protein, they would use it to immunize mice, then after 1-3 rounds of screening, you could obtain hybridoma clones.

There are some banks with hybridomas available for research, for example:

http://dshb.biology.uiowa.edu/

http://www.cellbankaustralia.com/ecacc-hybridoma/