1. No, listings are currently posted for the duration of the listing package, not determined by a specific date
2. If you're referring to the removal of the keyword "Search For" field on the main homepage search bar, there is no Vantage setting which would allow this to be switched on/off so it would require customization on your part if you were to remove it.
3. Listing type and category are part of the default listing requirements and as such do not have an option to be turned off. Claim listing can be removed via a setting, but upgrade listing cannot. Reviews also cannot be turned off via a setting, so any of those which cannot be set from the Vantage admin would require customization.
Ultimately either of the themes "could" potentially be customized to suit your needs, however my opinion based on the information given is that Vantage would probably be better suited. I say this because it seems the modifications would appear to be less involved than that required for ClassiPress, and also taking into account a feature yet to be implemented. Neither of the themes at this time include an events functionality, however this is a feature planned for a future release of Vantage. This being said, unfortunately I cannot confirm exactly when this feature will be available. I have seen a lovely example of a highly customized ClassiPress site used for events purposes which was created prior to Vantage being available, however this was some time ago and I cannot recall the URL at this time, sorry.