Thank you for your questions. The actual app can be used/seen only after signing in. Regarding your questions:
1. This was initially planned as a web-based application, and it still is. However, when it comes to mobile responsiveness, it's not great — something I've pointed out and am currently working on. I'll finish this work during the weekend. Creating native apps will probably make sense in future, too.
2. Yeah, as it's only the beta version at the moment, the pricing doesn't mention anything specific. I believe there will be three different pricing tiers. There will definitely be a freemium version with some limitations, e.g. a limit of one library and 100–200 books in library, and access to basic statistics only. I need to think more about the pricing in more detail, as I've only concentrated on building the product so far. However, in general, I imagine it to be as I've already described above.
3. This is a very good question, to be honest, and one that I haven't thought much about either. I would probably use a locally hosted application if it offered all the features that librari.io offers. However, I can think of some reasons why a user might want to use a web-based solution. Firstly, I assume that syncing across devices would be difficult when the application is hosted on only one device, unless it offers export/import functionality. Backup and reliability are other reasons why a user would opt for a web-based solution. I believe that the ability to share your library with other people or family members using a link, which gives them access from anywhere at any time, is a good reason to opt for a web-based solution.
4. I can outline the three most significant issues I encountered, which eventually led to the development of this app. The first is the outdated UI that most of them suggest (but of course, I'm not saying that librari.io's UI is the best). The second is the lack of library statistics and analytics (e.g. distribution tables of books, authors, etc. or content-wise and reading activity related statistics). The third is the lack of customisation. For example, the ability to add custom book, author and publisher data fields with different types, such as text, date and number, and then attach actual information to those fields when editing those entities.