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1. There is no need to include the day of the week. Just the date is acceptable.
2. I would NOT advise having the other party include the date when they sign the contract to avoid any chance of confusion as to when the non-disclosure restrictions became applicable. With that having been said, however, since the other party is signing the contract after the date when the disclosures were first made, the contract should contain a representation by the other party that they have not made any unauthorized disclosures.
3. You do not need to sign the contract unless there are some obligations placed on you, such as exclusivity of disclosure to this party until some stated date in the future. Absent any obligation on you, you don't need to sign the contract, but there is no real harm in it either.
4. Neither side has to provide any information -- they just need to sign the Agreement. If the other party is a person and not a company, then you would ignore the "Title" line.
I hope this helps.