Is the text on Tempest Djinn: "Tempest Djinn gets +1/+0 for each basic Island you control." considered an "ability"? Does that mean if Merfolk Trickster's triggered ability targets Tempest Djinn it becomes a 0/4 vanilla creature?
Yes, it's a so-called 'static ability':
604.1. Static abilities do something all the time rather than being activated or triggered. They are written as statements, and they’re simply true.
The ruling under the card in Gatherer confirms that:
Tempest Djinn’s ability that modifies its power applies only while it’s on the battlefield. In all other zones, it’s a 0/4 creature card.
so it's affected by Merfolk Trickster.
Is all the text on Tempest Djinn considered an "ability"?
No, the text on the card also includes its name, type, subtype, expansion, language, artist, copyright and trademark notice, and flavor text. None of those are abilities.
Tempest Djinn has two static abilities, Flying and "Tempest Djinn gets +1/+0 for each basic Island you control." If it loses its abilities, it ceases to have Flying, and will be 0/4.
All of a card's text is part of an ability, and only the card's text forms abilities. Note that the card's text is defined by Gatherer, which is a corrected, English version of the contents of the text box, without any of the italicized words.