Can a mass produced GPU profitably mine bitcoin if the electricity was "free" somehow?
If you mean "free" as in "solar", then the amount of time to reach ROI would be so long that it wouldn't make much sense.
(This actually doesn't happen as much as it used to twenty years ago with step-by-step inventory checkins made possible w/ RFID chips and barcodes combined with mobile network connections).
The hardware capex for mining BTC with GPUs would outweigh any 'free' power you have access to. You can't just focus on one aspect of this business in order to calculate your ROI.
It sounds like your scenario is more or less "free" power, but you're not going to truly profit; you bought too many solar panels and you're trying to mitigate the losses. (And maybe the overbuilding was on purpose, as insurance against grid trouble, but it still means a good chunk of money lost.)
What does this even mean? The average solar panel lasts 25 years and starts to degrade in efficiency before that. And then you have batteries which of course are also going to degrade and need to be replaced over time. Many countries are starting to get more serious about e-waste as well now that China has decided it won't take the world's trash any more so you might even have to occur a cost for getting rid of used panels as well.
There's plenty of costs in solar energy, so what does "free" mean here? Are you trying to take into account the possibility of selling excess energy back to the grid?