burden, the data for this study is limited and not enough to fully understand the emergence of the resistant allele.
All we know is that:
1) "these fish have managed not only to develop a resistance to the plant’s powerful toxin, but also to pass on their tolerant genes to their offspring, enabling them to survive in the face of otherwise certain death for their non-evolved brethren.".
2) "They found that the mollies annually exposed to the barbasco indeed were more resistant than the fish further upstream — to the extent that they were able to swim in the noxious water nearly 50 percent longer."
3) "Mollies able to tolerate the poisonous conditions survived and passed those traits to their offspring, resigning those that perished to their fate of serving as a ceremonial feast for the Zoque."
If you read the paper, you will realize:
1) There is no analysis of the genomic differences found between the resistant and the non-resistant fish.
2) There is no data on the effect that the toxin has on:
A) Gene expression
B) Epigenetic changes
So here are a few possible ways that a population with such a resistant allele can emerge.
1) Some fish in the original population express a gene (or a set of genes) that are able to detoxify/metabolize the toxin naturally. Those that do not, were killed and gave rise to a population of resistant fish.
2) None of the fish in the original population are able to detoxify/metabolize the toxin naturally. The toxin induced a set of genes that interfered with various control mechanisms, which in turn causes an increase in mutations to happen. Some of these mutations resulted in the formation of new proteins (or group of proteins) that are able to detoxify/metabolize the toxin. Those fish without the mutation were killed and gave rise to a population of resistant fish.
3) All of the fish in the original has a gene (or a set of genes) that are able to detoxify/metabolize the toxin, however, they are not expressed under normal conditions. When some of the fish are exposed to the toxin, epigenetic (or perhaps just genomic/proteomic/metabolomic) changes cause a change in gene expression that in turn results in the activation of the gene (or a set of genes) that is/are able to detoxify/metabolize the toxin (the cytochrome P450 family of proteins is a nice candidate). Those fish without the this adaptability were killed and gave rise to a population of that are more adaptable to the toxin.
Any of these ways or even a combination of these ways could be why there is now a resistant population. We just don't know what effect that this selection pressure (the toxin) has on the epigenetics as well as genomics/proteomics/metabolomics of the fish.
To reply to your "answers":
1) Of course the toxin has an effect on the activity of genes and gene expression. (I think you might have misread it, my bad, I meant which set of genes are caused to be up-regulated, meaning which genes' expression are changed)
2) Of course gene expression changes in response to selection pressure. That is a basic biological fact

. Gene expression does not stay constant and the toxin will DEFINITELY have an effect on gene expression. Again the data for mRNA levels, epigenetic changes, the effect it has on the proteome etc. is not known.
3) We know very little about how this allele emerged (see above).
4) Of course environment change characteristics in individual organisms. This is a biological fact. Read up on epigenetics.
Next time when you want to tell someone else they have "a bad understanding of evolution" or are confused, please try and understand their point of view first.