In SAFE Mode, since the Network Adapters don't load, Zone alarm doesn't either.
But it is still there as a Program File, in C:\Program Files\(ZoneAlarm or ZoneLabs)
As to Ad-Aware not appearing in SAFE Mode…
Your Desktop Icons may have changed size and arrangement due to the reduced video resolution in SAFE Mode. Ad-Aware Icon may actually be there, but it may be "pushed" off to the side/fringes of the Monitor Screen, such that you can't see it. The Ad-Aware Icon is a "short-cut" that you can view in your C:\DeskTop\, using Windows Explorer.
However, SAFE Mode may not have all of the Icons that your have configured for your Account Profile.
If you want an Ad-Aware Icon to serve as a "short-cut" in SAFE Mode….
Right-Click on any empty space of your SAFE Mode Desktop.
Select - New - Short-Cut
Then press "Browse" and navigate to C:\Program Files\Lavasoft\(Ad-Aware)
Find the Ad-Aware "executable" file that starts Ad-Aware (usually as follows) C:\Program Files\Lavasoft\Ad-Aware Personal SE\Ad-Aware.exe
Highlight "Ad-Aware.exe" and press next and then next again, to create a Desktop Icon for Ad-Aware on your SAFE Mode Desktop.
That should fix you up!
Best Regards