Previous Rez Key

Is there a way to obtain the previous key of an re-rez'ed object?

Only if you store it yourself.

key Mykey = NULL_KEY;

default
{
    state_entry()
    {
        if(NULL_KEY == Mykey) Mykey = llGetKey();
    }
    
    on_rez(integer num)
    {
        key id = llGetKey();
        if(Mykey != id)
        {
            llOwnerSay("I've been re rezzed with a different Key!");
            Mykey = id;
        }
    }
}

obviously if the script is reset then the key will be lost unless you write it into the description or some other 'permanent' store.

would an object on my own land be considered an efficient permanent inworld store? (what would other inworld-storage possibilities be?)

what is the maximum number of keys that such an object can store? is there a way to purge the object's store-database periodically, like "cron jobs" on the object?

Any script based storage, i.e. 'memory prims', will suffer from the same limitations.
For individual keys storing in the object description is possible but I wonder why you want to remember your old key anyway?

Storage within a script is limited to the amount of free memory (obviously) and will be dependant upon what else the script is doing. 16K does go a reasonable way if your careful.

Purging wil be down to simply emptying the list or reseting the script.

Other inworld solutions are manually argumented, i.e. the storage system has the ability to dump its contents to chat which you then manually cut and paste into a notecard.

amount of free memory of the user or of the linden server where the remote storage-object is served?

it's my understanding that the previous key can't be stored in the same de-rezzed object. though the re-rez of the de-rez'ed object returns to the same state it was before de-rez, all variables are lost?

When an object is taken into inventory it is effectively frozen at the point it was taken.
All variables are retained.

Each script is limited to 16K of memory for both code and data.

There is a 16k heap/storage space in each script. But you can use multiple scripts/prims and llMessageLinked to overcome this limit. (Also remember LSL uses by value assignments, so with list manipulations you usually have a lot less than 16k at your disposal)

The full state of a script is saved on derez/rez, including global variables.