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If a creature I control is being targeted by an enchant creature my opponent controls, can I equip it with an artifact that grants hexproof to counter the existing enchant creature?
Example: My opponent casts Kasmina's Transmutation on my Serra's Guardian. Several turns later I equip Swiftfoot Boots. Does the "hexproof" ability make Serra's Guardian an invalid target for Kasmina's Transmutation?
No. Hexproof prevents the creature from being targeted. Kasmina's Transmutation targeted the creature when it was cast, but after it's resolved it's no longer targeting the creature.
It's possible you are thinking of protection, which prevents the protected creature from being "Enchanted, equipped, or fortified by permanents with the specified quality." If you give your creature protection from blue, then Kasmina's Transmutation falls off, since a pro-blue creature cannot be enchanted by blue auras. Another possibility is if the aura enchants only certain things which no longer applies. For example if you cast Daybreak Coronet on your Kasmina-enchanted creature, and then opponent bounces the Kasmina's Transmutation, then Daybreak Coronet does fall off (since it can only enchant an already-enchanted creature, and with Kasmina's Transmutation off, the creature is no longer enchanted). Yet another possibility is if your creature turns into (say) an enchantment via One with the Stars, then Kasmina's Transmutation also falls off since it can only enchant creatures (it says "enchant creature").
Hexproof is none of these situations and therefore Kasmina's Transmutation remains attached. It will, however, stop your opponent from casting more auras targeting the creature.
If a creature I control is being targeted by an enchant creature my opponent controls, can I equip it with an artifact that grants hexproof to counter the existing enchant creature?
Yes, but note that equipping an artifact goes 'at sorcery speed'; normally you can only do it in your own turn when the stack is empty. See the Comprehensive Rules:
702.6a Equip is an activated ability of Equipment cards. “Equip [cost]” means “[Cost]: Attach this permanent to target creature you control. Activate this ability only any time you could cast a sorcery.”
You'll need an equipment that specifically has an ability to attach it to a creature you control (e.g. Cranial Plating, but then an equipment that grants hexproof) or another instant that is able to attach equipments.
Does the "hexproof" ability make Serra's Guardian an invalid target for Kasmina's Transmutation?
Not for the Kasmina's Transmutation that's already enchanting it; an aura only targets when it is played:
115.1b Aura spells are always targeted. An Aura’s target is specified by its enchant keyword ability (see rule 702.5, “Enchant”). The target is chosen as the spell is cast; see rule 601.2c. An Aura permanent doesn’t target anything; only the spell is targeted. (An activated or triggered ability of an Aura permanent can also be targeted.)
(emphasis mine)
