The decision on Durban Platform says that the outcome will be under the Convention and applicable to all parties. Does it mean that the principle of CBDR has been done away with in the new process?

As the Durban platform decision clearly says that the outcomes will be under the convention, both in the last para of the preamble and para 2 of the text; the principles of equity and CBDR will continue to apply. The Convention is built on the principles of equity and common but differentiated responsibility. Negotiation on the post 2020 arrangements will have to respect these principles even if there is no explicit reference or repetition of these principles in the text of the decision.
The principle of equity will become increasingly important because the arrangements will apply to all parties. Details will be finalized during negotiations.
The agreed phrase under the Convention is the strongest possible legal language which not only encompasses principles of ‘equity’ and ‘CBDR’ but covers also commitments of AI under Article 4.2 & 4.3 and the first priority of NAI being social and economic development and poverty eradication under Article 4.7.