Tasting a small amount: Although the full penalty for eating forbidden foods requires a minimum quantity (usually, the size of an olive), the Torah prohibits eating any amount.[1] Tasting forbidden foods (without swallowing) is prohibited rabbinically.[2]
Possibility of eating: Although not a simple matter, a person may, in a case of need, cook non-kosher food for non-Jews, and he need not be concerned that he may inadvertently eat from it.[3]
Cooking: The primary problem with cooking the milk and meat in your case is not the hana’ah (benefit) but the cooking itself. The prohibition of milk and meat is written in the Torah in terms of cooking and is stated three times to teach us that the cooking itself and, subsequently, eating or benefiting from the cooked mixture are all forbidden. Again, even cooking without eating or benefiting afterwards is forbidden. However, there are two pertinent areas of potential leniency:
1. Regarding fowl, which is considered meat only rabbinically, cooking with milk and benefiting therefrom are permitted, although eating is not.[4]
2. The prohibitions of cooking and benefit apply only when the meat and the milk are from kosher animals.[5] Thus, it is permitted to cook pork and milk even if you receive benefit. However, if the meat of a kosher species is forbidden because it was not slaughtered according to halacha, then it may not be cooked in milk from a kosher animal.[6]
There are complicating factors here as well. The Rama[7] says that it is forbidden to cook pork in milk because of marit ayin (people will not realize that it is pork). However, one who is in great need can rely on the Shulchan Aruch[8] and the Shach, who permit it.[9] In a context where people will not suspect him of eating the meat and milk, it is simpler to allow the cooking.[10] A Sephardic Jew could certainly be lenient.
According to many poskim, one may not even cook milk in a fleishig pot (or vice versa) that has been used within the past twenty-four hours.[11] Here, too, there is some room for leniency in a case of significant need. If you could somehow provide your own pots and utensils and had different categories (ideally: kosher meat, kosher dairy, pork and chicken, non-kosher meat, non-kosher dairy), it would be much preferred.