Pip, 65 60 bytes

OsX4FbPp:#_FIa^C X^Y"><+-.,[]"P[sX4pRXXsRA Uvbs(gU(y@?b)|9)]

The BF program and the nine explanation strings are taken as command-line arguments. Alternately, you can use the -r flag to take them from stdin. Replit! Or, here's a 61-byte equivalent in Pip Classic: Try it online!

Former explanation

New explanation pending... This is the explanation for the previous 65-byte solution.

Oi:sX4Pp:#_FIa^C X^Y"><+-.,[]"WpP[iPBsX#xx:POpsX#Jps(gU(y@?x)|v)]

First, the setup:

Oi:sX4Pp:#_FIa^C X^Y"><+-.,[]"   sX4                          Space character, repeated 4 times i:                             Assign to i (the indent)O                               Output it without trailing newline                   Y"><+-.,[]"  Yank that string into y (BF commands)                  ^             Split into a list of chars                 X              Convert to a regex that matches any one of those chars               C                Wrap the regex in a capture group             a^                 Split the first program arg on that regex                                (As in Python, splitting on a regex wrapped in a group                                keeps the matches of the regex in the result list)           FI                   Filter that list on this function:         #_                      Length of item                                (This gets rid of empty strings while not getting rid                                of "0", which is falsey in Pip)       p:                       Assign the result to p (the processed program)      P                         Print it with trailing newline

Then, the main loop:

WpP[iPBsX#xx:POpsX#Jps(gU(y@?x)|v)]Wp                                   While p is not empty:  P                                  Print (with trailing newline)   [                              ]  this list, concatenated:                                      1. Indent:          x                            Last chunk (initially empty string)         #                             Length of the above       sX                              That many spaces     PB                                Push those onto the end of    i                                  i (modifies i in-place)                                      2. Current chunk:             POp                       Pop the first item from p           x:                          Assign it to x                                      3. Padding:                    p                  Remaining chunks                   J                   Joined into a single string                  #                    Length of the above                sX                     That many spaces                     s                4. One more space before explanation                                      5. Explanation:                          y@?x         Index of current chunk in BF commands                                       (0 to 7, or nil if not found)                        U(    )        Increment (1 to 8, or nil)                               |       Logical OR                                v      Negative one (1 to 8, or -1)                      (g         )     Item in program args at that index