Here is a good rundown in English: https://www.basel.com/en/events/carnival
Not sure how many days you will find worth it - depends how into everything you are!
You should see at least one of the big parades - and if you only want to spend one day on Fasnacht, I'd pick one of the days with the Cortege. The Guggenmusik concerts are also fun (though loud) and it's worth checking out the lanterns at Münsterplatz when they are on display.
Everything is generally family friendly (although crowded, and also keep in mind that outdoor public drinking is allowed in Switzerland), but some of the events are very early/late. Morgenstreich is really cool with all the lanterns, but you have to stand out in the crowded streets in the middle of the night. There is always a special day for kids on Tuesday (Kinderfasnacht) - It's a bit less crowded and hectic because it's the day between the 2 big parades. Kids can buy confetti at the supermarket and join in throwing it around.
Basel's costume tradition is more about masks, so personally I like the creative and more varied outfits people come up with at Luzern Fasnacht better - but that is held a few weeks earlier. In any case, Basel is fun and worth seeing too. Just follow the advice and stay clear of the most congested areas (Marktplatz, Barfüsserplatz) if you are nervous about crowds during the main parades.