1. He bade the boy (to) work on the farm.

2. He ordered the boy to work on the farm.
3. He told the boy to work on the farm.
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Q1: Does #1 mean #2 or #3? Can we use both 'to work' and 'work' in Sentence 1?

Yes, all can mean the same thing. "Bade" (the past tense of "bid") is obsolete in this sense. To "tell" someone is to "bid" them to do something, but we don't use it that way any more.

http://www.merriam-webster.com/dictionary/bid

Sentence 1 can be interpreted to mean either Sentence 2 or Sentence 3, depending on the intended meaning of the speaker. This is because the verb "bade" can have a similar meaning to "ordered" or "told."

Regarding the use of "to work" and "work" in Sentence 1, both forms are grammatically correct and convey the same meaning. In this case, the infinitive form "to work" is used as the direct object of the verb "bade." However, it is also possible to use the bare infinitive form "work" without the "to" particle. So, both "to work" and "work" can be used interchangeably in Sentence 1.