I find that you cannot really play Anubis passively. You need to go all in with a few ability combos.
I have found the following combos very effective:
3 - 2 - 1
Throw down the Grasping Hands, then immediately Mummify. To begin with I was using Mummify first. However, doing it after means that the Grasping Hands will do more damage. The Mummify skill shot is also slightly easier because the opponent tends to freeze or delay to then change direction as you land the Grasping Hands. Once stunned, the Plague of Locusts can be used to deal additional damage on the easy target.
I would say that because the Plague of Locusts leaves you vulnerable (as you are rooted and relatively close), you shouldn't attempt this during team fights.
3 - 2 - ult
Much like the strategy above, except you are using your ult. With this method you are looking to kill off the opponent. I wouldn't try this combo unless I was confident in getting the kill.
3 - 2
This simple combo allows you to knock a little health off the enemy god. I use this if I don't want to risk using my 1 or ult. It is also useful to work out if you are doing good damage to a particular god.
In terms of escaping, I use the following:
You can cancel your 1 and ult. This is very useful if you are about to get ganked or you miss your 2 (Mummify).
Unfortunately, you just got to get good at the skill shot. It isn't too hard once you stop panicking when an enemy god gets close. Additionally, try to keep Mummify ready for situations that may lead you to being ganked or ambushed. For example, going for jungle buffs.
There may be situations where you can go 2 - 1 on an ambush. Mummify to stop the threat then hit them with the Plague of Locusts. However, this is only going to work if you think the damage you deal is enough to push the enemy back.