sponsorship of parents and grandparents for Canadian Permanent Residence

[canuck_in_uk]

however, there is one thing im not clear about: the rule is the undertaking is for 20 years. while my parents are here as permanent residents, can they start applying for citizenship? if yes, when can they do that?

most importantly, once they become citizens, does anything change in terms of entitlements? meaning, are they entitled of financial support from the government (social assistance) or is it the sponsor's obligation to cover for EVERYTHING, even when they become Canadians, throughout the 20year period?

They can apply for citizenship once they meet the requirements.

This is very clearly answered at the beginning of the guide:

Important information: The undertaking is an unconditional promise of support. For example, the granting of Canadian citizenship, divorce, separation or relationship breakdown or moving to another province does not cancel the undertaking. The undertaking also remains in effect even if your financial situation deteriorates.