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VAMPLIERS. World's Best Pliers. 8" Pro Lineman's Screw Extraction Pliers. Specialty Screw Extractions Pliers. Extract Stripped Stuck Security, Corroded or Rusted Screws/Nuts/Bolts https://www.amazon.com/dp/B00LMOAYR2/ref=cm_sw_r_cp_api_i_MzupCbHE9H75V
If it sticks up beyond the surface at all these will get it https://www.amazon.com/VAMPLIERS-Linemans-Extraction-Specialty-Extractions/dp/B00LMOAYR2/ref=sr\_1\_6?crid=2ZKHTQF59UGRE&keywords=vampliers&qid=1643917724&sprefix=vampliers%2Caps%2C142&sr=8-6&th=1
VAMPLIERS. World's Best Pliers. 8" Pro Lineman's Screw Extraction Pliers. Specialty Screw Extractions Pliers. Extract Stripped Stuck Security, Corroded or Rusted Screws/Nuts/Bolts https://www.amazon.com/dp/B00LMOAYR2/ref=cm_sw_r_cp_api_i_bq97Db6EHQQSB
No, you're fine, you haven't damaged any of the copper, just taken off the protective coating.
Yeah, those screws can easily strip out. Just to make things more difficult, they also have very shallow heads, so it is near impossible to get something to grip, to loosen it.
If you see any screws with a small dot indentation between the cross, then they JIS screws, they are NOT Phillips. Using a Phillips screwdriver, will strip them out like what has happened to your device.
JIS screws can be found on Japanese and Korean-made devices. I'm not so sure about Chines-made.
No, you're fine, you haven't damaged any of the copper, just take off the protective coating.
Or the cheaper version...
From what I know, the engineer brand are the exact pliers of the Vampliers but have a less cool sounding name.
I have a pair of these. They are slightly smaller and for the amount of times you'll use them you probably want a lighter set to throw into the tool bag rotation. They work great.
When you bodge the inside, you can always try bodging the outside.
Had good luck with these, plus the usual suspects, heat, penetrating oil.