Let's digress by looking at how the meaning of "computer" developed during the 20th century. A "computer" used to be a person, somebody doing computations; devices eventually took over the job. This unlocked an explosion in the complexity of business applications that required a lot of highly reliably computing power, from, say, payroll accounting, to sophisticated modelling of all kinds of processes.
You could paraphrase compute, the verb, in its various old and new flavors as "count together" or "evaluate together".
Now, let's tackle your sub-questions backwards.
Re 3: The prefix means "into".
Re 2: There's a semantic overlap, which is "reckon" (or "think"). No shift of meaning appears strictly necessary, although derivation always involves at least a little bit of semantic specialization.
Re 1: Evaluating something (or somebody) may be as simple as adding together (and ticking off) some numbers, or it may involve much more complex modelling (of that person). It's a mental process either way. When such an evaluation is finished, somebody may impute its conclusions to the person who was the subject of the evaluation: treat the conclusions as a fact firmly sticking on that person.
(This way of using our brains is so boringly common among humans, that the mere mention of anybody "imputing" anything typically implies the the conclusions weren't necessarily accurate or universally shared, and that somebody else may eventually dispute them, or try to come up with a different account.)