How can I tail a zipped file without reading its entire contents?

If you have control over what goes into the file in the first place, if it's anything like a ZIP file you could store chunks of predetermined size with filenames in increasing numerical order and then just decompress the last chunk/file.

BGZF is used to created index gzip compressed BAM files created by Samtools. These are randomly accessible.

http://samtools.sourceforge.net/

No, you can't. The zipping algorithm works on streams and adapts its internal codings to what the stream contains to achieve its high compression ratio.

Without knowing what the contents of the stream are before a certain point, it's impossible to know how to go about de-compressing from that point on.

Any algorithm which allows you to de-compress arbitrary parts of it will require multiple passes over the data to compress it.