Will my spouse divorce me if I ignore them or pursue others?
There is no divorce option in the game as of yet, but it's being considered for the next update.
Friendship with your spouse works largely the same as friendship with any other NPC, with two more additions: if you gift an item to another bachelor/ette, your spouse will get upset and lose some friendship, letting you know that they saw you "secretly giving a gift" to someone else; similarly, declaring your love to someone with a Bouquet will lower friendship by a bigger amount (~2 hearts).