personally I would look for a more positive based trainer not one that relies on e-collars and prongs alone to "train" a dog. hopefully she gave you a plan on how to train as well as the prong. It is VERY normal for a dog to be "perfect" when you stick a new tool on them and then as they get used to it start some old habits. that's why you need a training plan not just a tool.
I would highly recommend trying to train him using more positive based techniques VS strictly aversives (spray bottle, prong, e-ccollar). Especially as he's new and just settling in and possibly showing signs of stress (the panting). I am not saying never correct, just not using those as a go-to. Set him up to succeed (put the cat food where he can't reach - i can't imagine having a bolw of cat food out where my dogs could just get to). VS setting him up to fail (leaving the litter and food out where he can easily reach) and "correct".
high tail can mean alert (vs a low calm wave). holding and nipping is "normal" but not really "appreciated" or "appropriate" at the dog park adn could get him in trouble. Might be ok with some dogs, not with others.
an e-collar is not something you stick on a dog and buzz whenever they do something you don't like. that could create some major issues.
some good sites wtih tips and info on training:
Some sites with how to teach your pup to walk nicely on leash (positive trainers): Pet Education: Loose Leash Walking Summary
or Dr. Yin’s Animal Behavior and Training Videos | Dr. Sophia Yin, DVM, MS
Dog Star Daily
Victoria Stilwell Positively | The Official Victoria Stilwell Website
Animal Behaviorist | Dr. Sophia Yin, DVM, MS