As for seeing what books you have in calibre from your tablet/phone, what devices do you have? If they are Android devices, I suggest you get
Calibre Companion, developed by a MobileRead member and sometimes developer of calibre. It is an excellent app for managing your ebooks, and very popular here, and one thing which users have discovered is that it is easy to use it as a simple catalog as well -- simply add a blank TXT format to each of your books -- see
HERE, #7 -- then send the TXT to Calibre Companion.
Calibre Companion will "have" all your books, and show you their metadata and let you search through them etc. etc. but it will only take up ~1KB per book since they are all just blank TXT files.
You can add the actual EPUB/AZW3 for the books you do want, there are several ways to download your books with Calibre Companion.
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Alternatively, simply leave calibre itself turned on and set up the Content Server for remote access (Dynamic DNS + router port forwarding), and Calibre Companion can browse the live OPDS catalog and download books as desired.
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Alternatively, if your calibre library is synced to Dropbox, OneDrive, etc. then Calibre Companion can access your library from there, without having to use a running Content Server and setting up Dynamic DNS + port forwarding.
See:
http://cc_faq.multipie.co.uk/index.p...ion=show&cat=2