Does the word "makrooh" (disliked/reprehensible) mean that Allah dislikes this thing, and does the same meaning apply to the word "mustahabb" (recommended/desirable)?

Makrooh means that which Allah dislikes, whether it be a dislike of prohibition (Karahat Tahrim) or a dislike of discouragement (Karahat Tanzih). The word "makrooh" is often used for that which is forbidden (haram), and it may also be used for a dislike of discouragement. As for Mustahabb, it is that which Allah Almighty loves, and it is that which He commanded as a matter of preference, and Allah loves and approves of it.