pwd -P will give you the physical directory you are in, i.e. the pathname of the current working directory with the symbolic links resolved.
Using df . would give you the df output for whatever partition the current directory is residing on.
Example (on an OpenBSD machine):
$ pwd /usr/ports
$ pwd -P /extra/ports
$ df . Filesystem 512-blocks Used Avail Capacity Mounted on /dev/sd3a 103196440 55987080 42049540 57% /extra
To parse out the mountpoint from this output, you may use something like
$ df -P . | sed -n '$s/[^%]*%[[:blank:]]*//p' /extra
To parse out the filesystem device used, use
$ df -P . | sed -n '$s/[[:blank:]].*//p' /dev/sd3a
I believe some Linux systems also supports
findmnt --target .
(where --target . can be replaced by -T .) or, for more terse output,
findmnt --output target --noheadings --target .
(where --noheadings may be replaced by -n, and --output target may be replaced by -o target) to get the mountpoint holding the filesystem that the current directory is located on.
Use --output source to get the mounted device node.
pwd -P, but ok.