I.I doubt he would be here tomorrow.
II. My parents are all doctors.
a.Should I must change "would" to "will" in the first sentence?
Yes. A native speaker would say, "I doubt if he'll be here tomorrow."
b.Is there any thing wrong with the second sentence?
'all' refers to the whole quantity or extent of a particular group or thing. Since we only have two parents, technically, you might think you'd be right. However, to a native speaker, 'all' suggests a minimum of 3, so it sounds very odd to use 'all' in relation to one's parents in this sentence, instead of 'both'.
My parents are (both) doctors.
Both (of) my parents are doctors.
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