Does not intitiating a variable use memory?

For example

local timer t

If I put that at the top, is it using a handle or anything? Should I set t = null at end or something?

Just set it to null at the end of the function to be safe.

It isn't using anything since there's basically nothing to point to.

All variables in Warcraft 3 use 4 bytes of memory. Declaring a variable will reserve that memory. For globals, it will be reserved at map start. Locals are probably stack-allocated, but I don't know about all the complexities of the JASS VM. Agent-type handles are pointers. (as well as a few other handle types, but not all handle types.) The object an agent-type handle points to is separate from the variable containing the 4-byte pointer.

You null reference-counted handle-types (basically, agent-types) because the VM is bugged and will not reduce the reference counts of things held in local variables when a function returns. You only need to null local variables which contain agent-type handles, and you only need to do it before a function returns. (Setting them to any other value reduces the reference count of the agent, and increases the reference count of the new value.)