1.
No there isn't (yet) such possibility.
2.
New
(still "hidden") feature as from version 2.51
build 1022:
(rightclick >) Options > Preferences
In "Preferences" keep [Shift] depressed while you click on "Subtitles".
Now click on Tab [Online subtitles]
At the bottom you will now see a box with the label "Save downloaded subtitles to"
If you want BS.Player to save subtitles to movie file folder in subfolder "Subs" select
"%P\Subs\%F-%L%SE". If you want to save to user folder select
"%P\%F-%L%SE". (Those two options are pre-defined in BS.Player.)
N.B.: The "translation" of the variables used (and some more) is as follows: %P - movie folder %F - file name %E - extension %S - subtitle name %L - subtitle language %SE - subtitle extension