Do native English speakers use the word 'notif' to mean ‘notification’ or ‘alert’?

To answer your direct question, no, 'notif' is not used at all in American English (I can't speak to other varieties), in speech.

There's a general question here though and that is how, in general, English abbreviations are made.

The bulk of abbreviations in English tend to be acronyms, the initials of the words making up the phrase ('USA' for United States of America), or removing vowels and inferable consonants, only for writing ('abbrv' pronounced 'abbreviation').

Of those that are not initialisms, the most common method is to use the first syllable, ('lab' for 'laboratory', 'teen' for 'teenager'). For a counter example, 'computer' doesn't have a good abbreviation; the first syllable is unstressed and I don't know why but 'puter' just sounds awful and anyway no one says that out loud.

There are some very rare instances where an unstressed final syllable is done ('za' for pizza).

But on the whole, if there is a word shortening, it is the first syllable and it is usually closed and accented.

The general rule, if you can call it a rule, when abbreviating is that the result should sound natural according to a languages phonology. Short words in English tend to be CVC (ConsonantVowelConsonant). French syllables try to avoid closing, so tend to be CV (ConsonantVowel).

You may wonder then what is the abbreviation for 'notification' in English speech (because certainly that word is uncomfortably long in any language). And the answer is probably ... 'alert'. Yes, I realize that is a different word, so not really a shortening. But there is no shortening of 'notification' that people use in English speech.

Of course, in writing and especially in texting, all sorts of ways to shorten typing are used: 2 for to, r for are, etc. There is enough evidence of 'notif' in texting, whether by logical reinvention every time or by culture, that it should be recognized as a repeatable pattern. But in speech, 'notif' just hasn't caught on at all.

I've never heard it, in fact I wouldn't even vocalise it to myself as "notif" if I saw it on a device. I'd just think "I've got a notification" or "which programming language is that, does it mean 'elseif'?".

Having said that it could well be current with the hipster/pseudo-cool/trendy crowd who use phrases like "totes amazeballs"; I wouldn't know.

According to my chat histories I've used the word "notif" at least 3 times in the last month, and I've definitely used it in real life. I'm also an Aussie, and we like to shorten our words, which I think is totes amazeballs.