Can I activate Hunting Instinct if...

1.) ...I special summon Gilasaurus and my opponent chooses to special summon a monster from their graveyard?

2.) ...my opponent activates Magical Dimension, special summons, then chooses to use Magical Dimensions' effect to destroy a monster?

3.) ...my opponent activates Magical Dimension, special summons, then chooses NOT to use Magical Dimensions' effect to destroy a monster?

4.) ...my opponent special summons a monster to my side of the field (Lava Golem, etc.)?

OK, I'll try this one...

Hunting Instinct's Text:
Activate only when a monster is Special Summoned to your opponent's side of the field. Special Summon 1 Dinosaur-Type monster from your hand.

1. Yes, you could activate Hunting Instinct since the last thing to have happened is the special summon of your opponent's monster.

2. No, you would not be able to activate Hunting Instinct since the last thing to happen was the destruction of a monster and not a special summon of your opponent's monster.

3. Yes, you could activate Hunting Instinct since the last thing to have happened is the special summon of your opponent's monster.

4. No, you would not be able to activate Hunting Instinct since the last thing to happen was not a special summon of a monster on your opponent's side of the field.

Thank you for the help.

Sorry about the last question, I didn't have the card with me at the time, so I couldn't check the text.

Another thing, can Hunting Instinct be used when the opponent Fusion/Ritual summons?

Ritual and fusion summoning all fall under the category of special summons.

You would be able to play Hunting Instinct.

You are correct but the question from Lux Ultima's first post was:

4.) ...my opponent special summons a monster to my side of the field (Lava Golem, etc.)?