"As soon as there are martians at points A,B,C such that triangle ABC contains the center of the field..."
Are the three points, A,B,C any set of three random points on the circumference of the field from an increasing permutation of triangles that would enclose the field's center? That is, if Farmer Brown has not been transported after the appearance of three alien zoologists, a,b,c, but, a minute later, a fourth martian, d, landed, there are four permutations of triangles, such that zero, one or two of the four permutations that involve the four landed martians form triangles that enclose the field's center point. Would each of the triangles that enclosed the field's center be considered triangle ABC (I.e., more than one triangular transportation zone might exist)?
Is it possible that a martian may land on an already occupied point [a Dorothy-Gingema event], and are martian's considered point-like beings for calculation of the probability?
Not quite true. "The number one is a unit; it is neither prime nor composite." Prime and composite are terms that are applied to positive numbers (though the definitions can been extended to include negative numbers -- as associates to the positive, i.e., the negative number is deemed the same prime or composite as the positive number by the extended definition [refer to the Prime Pages FAQ "Can negative numbers be prime?"]). A composite number has been defined as any positive integer that has at least two prime factors.
Ignoring the re-roll part and probability, rolling 2-dice and taking the product does not create a uniform random integer. Some values will occur more often than others in that manner (1x4 & 2x2 both equal 4, e.g.),