[–] Citizen 0 points 1 point 1 point (+1|-0) ago
In short, yes. And to answer your second question, some malware is written for the challenge, but most modern malware is written for profit.
The first self-propagating malware for IOS was seen in 2009.
The first self-propagating malware for android was seen in 2014.
Thankfully, self-propagating worms are very few and far between.
There are also malicious programs that require user installation, such as flashlight apps that secretly spy on the user, but that's a different category of malware.