My idea of the word stalking is an action showing that you like someone and wants to know more about them; and even try the most extreme actions

Dictionary meaning

1. To walk with a stiff, haughty, or angry gait: stalked off in a huff.

2. To move threateningly or menacingly.

3. To track prey or quarry.

v.tr.

1. To pursue by tracking stealthily.

2. To follow or observe (a person) persistently, especially out of obsession or derangement.

3. To go through (an area) in pursuit of prey or quarry.