What does the word "carcasses" mean in the following context?

"In addition to these denied rights, the workers of these educational institutes are working in miserable conditions: the safai karamcharis (cleanliness workers) begin their days by cleaning the carcasses of toilet waste."

Militate?

"As the agitation grew in scale, the workers started to ‘militate,’ against the administration."

Fund?

"Surya also threw light on the non-planned expenditure fund that is reserved for emergency purposes. However, these expenses are not available in public view either."

Create a binary?

"Such comments by those in power depict that they are trying to create a binary between the welfare of the students and those of the workers."

Administration-company nexus?

"A mess manager named Abhishek (a category often considered apart from the workers) of Lohit Hostel, who was active throughout the strike, was arbitrarily terminated by the administration-company nexus post the strike."