1. I move that a vote be taken on this.

2. I suggest that a vote be taken on this.
(Does #1 mean #2?)

3. He suggested that she was a professor.
(Is this sentence correct? What does 'suggested' mean in this sentence? What other words can we use?)

4. He suggested that she might a spy.
(Is this sentence correct? What does 'suggested' mean here?)

1 is more formal than 2. A suggestion is one person's wish or opinion, but to move (to make a motion) is a formal action at a meeting that needs to be seconded and then voted on. It may pass or it may not pass, but the process in a formal meeting needs to take place.

http://www.rulesonline.com/

3. This sentence would make better sense if you wrote this: He told us that she was a professor. The verb "suggest" doesn't work well here.
http://www.dictionary.com/browse/suggest?s=t

4. In this sentence, "suggest" is a good verb. It means he thinks she's a spy, but he's not sure. He can't prove it.

1. Yes, the sentence "I move that a vote be taken on this" means the same as "I suggest that a vote be taken on this." Both sentences express the idea of proposing or recommending that a vote should be conducted regarding a particular matter.

2. The sentence "He suggested that she was a professor" is correct grammatically. In this context, 'suggested' means that he put forward the idea or opinion that she was a professor. This means he proposed or hinted at the possibility that she holds the occupation of a professor.

3. The sentence "He suggested that she might be a spy" is correct grammatically. In this context, 'suggested' means that he offered the idea or opinion that she could potentially be a spy. It implies that he proposed or hinted at the possibility that she is involved in espionage or covert activities. The word 'suggested' can also be replaced with words such as 'implied' or 'insinuated' to convey a similar meaning.