FFmpeg with Automator & ask Start and Stop parameters
You asked "Is it possible to set the two parameters using a popup window?" and the answer to that is yes.

Here is one example of how it could be done:

In between the Ask for Finder Items action and the Run Shell Script action add a Run AppleScript action with the following AppleScript code:

on run {input, parameters}
    display dialog "Enter the start time and length:" default answer "-ss 00:00:00 -t 00:00:00" buttons {"Cancel", "OK"} ¬
        with title "Set FFMPEG Start Time and Length: -ss 00:00:00 -t 00:00:00"
    set beginning of input to text returned of result
    return input
end run


Then in the Run Shell Script action, change the script to the following code:

start_time_and_length="$1"
shift

for f in "$@"
do
    /usr/local/Cellar/ffmpeg/3.2.4/bin/ffmpeg -i "$f" $start_time_and_length -c:v copy -c:a copy -f mp4 "${f%.*}.mp4"
done






How this works:


The Ask for Finder Items action passes a list of filesystem objects to the next action.
The Run AppleScript action uses a display dialog to add the start time and length to the beginning of the list passed to it from the Ask of Finder Items action.
The Run Shell Script action receives what was returned from the Run AppleScript action, in this case the value of return input as a list in which its first item is the text returned from the result of the display dialog, being the start time and length. This gets set to the start_time_and_length variable and then shift is used to remove it from the list that gets passed to for f in "$@" to process the remaining items in the list.




Note: If you have a issue using the AppleScript code, shown above, then you could use the following as a workaround:

on run {input, parameters}
    set tempList to {}
    display dialog "Enter the start time and length:" default answer "-ss 00:00:00 -t 00:00:00" buttons {"Cancel", "OK"} ¬
        with title "Set FFMPEG Start Time and Length: -ss 00:00:00 -t 00:00:00"
    set end of tempList to text returned of result
    repeat with i from 1 to (count of input)
        set end of tempList to item i of input
    end repeat
    copy tempList to input
    return input
end run