If the rod gets stuck then it'll begin drawing lots of current and likely to overheat,meaning you wont be able to get decent welds out that stick. So if your efforts to detach it don't work within a few seconds I would depress the rod release lever while pulling the holder quite hard. That releases the rod fairly sharpish. Yes you will get some arcing, but as the holders are usually aluminium it wont stick.
Bend back/forth to detach rod from plate. Once you've got the rod detached from the base, I've found it often helps to give the end a quick once over with a file, seems to rub off excess electrode/flux and helps with restarting without getting stuck, when the flux has broken off around where it had stuck. Can also help if the electrode refuses to restart (current setting too high for rod?)
You'll get better at not getting the rod stuck. Took me about 4 sessions of 2hours to begin to get the knack of keeping the arc lit. But then I was doing it without an instructor. Still haven't mastered consistent welds though. I'm forever getting flux mixed in the weld! I'm probably using rods that are too thin/current that's too low for the thickness of metal, but all I have is a domestic plug socket, and I can't draw too much without tripping out the all important fuse
You're getting sparks when you pick up the plate because you're interrupting the circuit by picking it up. That suggests you're working on a grounded workstation, rather than grounding the work piece directly. I clamp the work to the metal plate I place over my bench to protect it, and then earth BOTH with the earth clip, Makes it difficult to lift the plate, and with more complicated welds helps keeps the parts to welded aligned, even if the electrode gets stuck/needs removed. Don't worry the arrangement you're using is probably more correct. When running higher currents the current flowing through both the workpiece and table will produce a strong EMF which should help ensure the parts are kept in really good contact. (same kind of tthing as when the spark starts and the electrode is pulled towards the work)
I'd really try to avoid sparking between plate and work surface. It'll not be a particular clean break, and it'll cause a small amount of damage to the surface of your work and over time it'll scar the work surface. Sparks pack a surprising amount of punch in a very small area. Indeed there's a form of machining called Electric discharge machining that utilises sparks to remove metal in a controlled way. Far better to have the spark between the consumed electrode, and the easily replaced electrode holder. Besides with one hand needed to hold the plate, it's all to easy for the electrode holder to be inadvertently placed down on the earthed table while you are picking up the old electrode. Big BAD spark then!
Another reason why I don't like about the idea of picking the plate up with one hand while holding the electrode in the other is you've potentially got a direct path straight across your body/heart. Now 50V (or thereabouts) rarely causes any problems, and your gloves are supposed to insulate anyway. But "hand to hand path" carries the greatest risk of electrocution.Why risk it when there are alternatives without that risk?
If you do do as you instructor says and want to pick the plate up to remove a stuck electrode, then to prevent unwanted sparks/remove the electrocution risk. I suggest turning the welder off first. No current=no spark=no damage anywhere.