Yes, you could even delete all versions of Harem Hotel on your PC/Mac and your saves will remain in a separate folder in appdata.
Yes, in the save menu, you can rename "Page 1" to anything you would like by clicking on it. This allows you to organize your saves any way you would like.
There is no limit on the amount of saves you can have in harem hotel. It's 100 save slots per page, with an infinite amount of pages you can rename. You can also go left in the save menu for auto saves.
Thank you for playing so much!