I think KPhotoAlbum (available only in LINUX as far as I know) can meet most of your basic requirements, if I understand them correctly. The documentation is not as clear as for some of the commercial Windows software options. The basic organization is by EXIF date (if you choose this option), but you can organize it by folders, or by "tags" (e.g. you can look at all the photos in which "Fred" appears in photos taken in "Italy", etc.). Of course the big job in any such package is to properly organize the folders containing the photos and to enter the information about the subject, the people or objects contained, the locations, etc. In KPhotoAlbum (KPA), the terminology is "Annotate" which is similar to "Tag" in other software but more powerful. KPA does NOT do any editing of photos itself. It does not change the photos on disk, but allows you to invoke external photo editors to modify the actual photo. You can mix photos and video clips with no problem.
You can also view as slide shows, etc. and create web pages although I have not done much of that, and I think the html output is a bit primitive compared to something like JAlbum.