No . I use the squirrel and the log trick, like 'The squirrel went past the log", and 'do' does not fit that rule. 'The squirrel went do the log' is not correct.
Do is a verb the past tense is did
No, "do" is a verb, not a preposition. Prepositions are used to show the relationship between a noun (or pronoun) and other words in a sentence. Examples of prepositions include "in," "on," "under," and "beside."