Under Biden's presidency, are we going to see individuals given limits on how much energy they use and fines when they go over?

We do that in California already!  Both electricity and gas are 'tiered', meaning you pay one price for the first xx watt hours or therms of gas, and a higher price for after that.  We also get a report at the end of the year to show how much we used compared to the average home in our county.

This is an alternative to simply powering down the whole grid for a few hours when total use goes above a certain level.  They do that in some countries!  Would you like that better?

Sure. What do you think "smart" meters are for? Yes, you'll be limited. Not that we don't have the energy, but to make you understand that you can't have everything that you want. The Paris Accord limits your use & the US will pay for limiting other countries pollution (About $100 Trillion).

Probably not. Everyone knows Americans are too glutinous. They're more likely to try to shift towards more efficient energy sourcing and distribution, which of course will be met by backlash for no real reason, and we'll just be stuck as a sinking ship as the world progresses past outdated energy sources.

No evidence of that. Trump making crap up isn't evidence.

Well, apparently, rightards are going to make up stupid and false sh*t just as they did with Obama and Clinton.

‘Although it is not true that all conservatives are stupid people, it is true that most stupid people are conservative.’ John Stuart Mill   

Might happen.....Under our Democrat regime in California a few years ago, we were penalized for going over our average water usage. This was early done if you had a pool like myself. 

Lets put this way. Governments, be it State or Federal have a way of achieving this by way of taxes. Raise the taxes, and people will purchase less of that commodity or service.  

Possibly, the green new deal might be a thing by then.

No. Quite simply, no.