1) In your sentence, "is" is necessary. The combinations of tenses in sentences like this are somewhat fluid, but I think I would usually say:
"I think (that) it is best (that) we do this tomorrow."
"I thought (that) it was best (that) we did this tomorrow."
The construction without "is" that you may be thinking of is:
"I think it best (that) we do this tomorrow."
(Note: no "that" after "think".) This is a special type of construction, whose grammatical name I'm afraid I don't know, that you can use with verbs such as "think", "consider" and "deem".
2) "I am hungry, so hungry that I ate my friends’ lunches."
This is OK, but I think I would personally use a dash rather than a comma.