The word translated here as "form" refers to the the true inner nature of something. AT: "He was in nature God" or "He was divine" or "He was truly God"
Here "equality" refers to "equal status" or "equal honor." Paul is speaking here of equality with God the Father as if it were something that Christ could grasp with his hands. As the UDB makes clear, during Christ's time on earth, he did not cease to be God; instead, he ceased to act as God. AT: "he did not think that he had to have the same status as God" (See: [[rc://en/ta/man/translate/figs-metaphor]])
Paul speaks of Christ as if he were a container in order to say that Christ refused to act with his divine powers during his ministry on earth. (See: [[rc://en/ta/man/translate/figs-metaphor]])
Paul speaks of death here in a figurative way. The translator can understand "to the point of death" either as a metaphor of location (Christ went all the way to death) or as a metaphor of time (Christ was obedient even until the time that he died). (See: [[rc://en/ta/man/translate/figs-metaphor]])