I blame the editor. This is by any stretch of indulgence a terrible passage, which requires minute an time-consuming rereading to get anywhere near what it actually means.
i. We have the confusing repetition of the word 'for'. It seems to be equivalent to something like 'in relation to'. It is making the simple stipulation that the effect of natural selection is a function not just of the characteristics of the species itself but also of the environment in which the species exists (whether there is enough of the right food, whether it is among superior predators, its rate of breeding etc...).
ii. So if the writer wants to add a further explanation, it would be better to end the sentence here with a full stop and move on to the explanation. But here is where we run into trouble. We are not talking about animal species in this sentence, but of genes and genotypes generally. The next confusion arises from the use of 'them' for "any* mutation* or gene combination ". "Them" should be "it". This is because the sentence "A is big or B is big is equivalent to "A or B is big.
So the core of this sentence [that is, omitting the long participial phrase: "contributing ... r)] should read as follows.
For any mutation or gene combination ... will be selected over <'over' means 'rather than'> genotypes contributing fewer of their kind to successive generations.
There are still several problems with the passage.
iii. The original sentence is written as if the terms gene and genotype were synonymous, which they are not.
Is there any way of salvaging this dreadful sentence? The best I can do is this.
Natural selection will tend to maximize r for the environment in which the species lives. This is because any mutation or gene combination which increases the chance that any genotypes possessing them will contribute more individuals to the next generation (that is, of increasing r) will be selected over genotypes which contribute fewer of their kind to successive generations.
I think that this must be what the author means to say. But it is still opaque, and needs to start again from scratch.
To return to your questions:-
No. The second 'for' must be the explanatory conjunction.
"possessing" is what is often called a gerund (a verbal noun, in this case in the possessive mode, after 'of'). It is equivalent to "the change that genotypes which possess them...". Matters are made worse by using two '-ing words, the first a gerund and the second a participle, so close together.
See my answer to 2. It is bad writing.
The subject of will be selected is mutation or gene combination.
Your questions are all spot on.