Responding to Hothead's questions ...
I think an AI should use its own Matrix attributes all the time, as a technomancer would. Like any hacker, they're free to take any number of Firewall- or Data-Processing-based actions on the grid; those are all perfectly legal. The Overwatch clock only starts ticking when they take an Attack- or Sleaze- based action (see Illegal Actions, SR5 p.231), or start using advanced programs (Data Trails, p.157).
I wanted to simplify the Home mechanics, so optimization is a one-time +1 bonus to the main Device Rating or Host Rating, which lasts as long as the AI makes its Home there. This doesn't affect any other attributes, it doesn't change the lifestyle cost for renting space in a host, and it doesn't allow the AI to raise its Depth rating higher than the original device or host rating. (It might give host owners an incentive for renting space to an AI, though.)
Think of a Home device or host as the AI's "body," and treat its interaction with other external devices the same way you would a metahuman hacker or rigger. An AI can focus its attention anywhere in the Matrix like a hacker would. Where the hacker or rigger leaves their body behind in the van or mom's basement; the AI leaves its source code behind in its Home.
I suppose an AI could use another device like a cyberdeck or RCC, same as a technomancer could: They would be restricted to the device's attributes and program slots instead of their own. They would use that devices's Matrix condition monitor, and reboot that device to clear their Overwatch score.