How long do the invites last?

When you build an Inn, a guest will come. This guest stays for 3 days, starting with the day he arrives. If you click on Manor -> Buildings -> Inn, it will tell you how much longer he will be there "This guest is going to rest here for another x days.". Note that when it says 1 day, that means that at the end of the current day the guest leaves (=midnight game time)!

If you have  used an invite before the current guest leaves, the invited one will immediately replace the first guest and in turn stay for 3 days. If you fail to send out an invite before the guest leaves, a random guest will show up at the Inn, most likely this will be just a "Traveler", who doesn't do anything except pay 50 silver per day.

You can only use 1 invite at a time. You can use it right after the first guest came and 3 days later the invite will take effect. If you use a new invite before the new guest comes, the first invite becomes invalid. (Say you have a traveler in your Inn and you use a Clairvoyant invite. Once the Traveler leaves, the Clarivoyant will replace him. However, say you now use a Captain of Rangers invite before the Traveler leaves, the Clairvoyant invite becomes void and instead a Captain of Rangers will show up once the Traveler is gone.)

Apologies, if this is more than you wanted to know, but I hope it still helped you ;D

Thankyou that was helpful.