If you have an old analogue meter it will run in reverse, but this is illegal (you are reducing your metered usage of grid electricity, but the price of that includes grid transmission costs, taxes etc). The modern ones have a separate meter if you want to feed it to the grid, but it's not worth it, there are some fees for that so you'd end up with a few bucks every year.

So the way it works, you plug it in, and your appliances can use it and not the electricity from the grid. The excess you don't use gets fed in the grid, generally for free. You save basically on all the taxes, transmission costs etc, which are the majority of the price, if you use your own electricity. The more you can use, the more you will save.

If your home is fully solar powered and you are making more then you're using at the moment, then yes, the meter counts backwards.

Most of the time though, your production will be less than your consumption, so your meter will simply not count the watts you don't pull from the grid.

Digital non-smart meters don't run in reverse. Or at least mine doesn't.

I've ended up with three dumb meters: one main one, one that measures energy off the solar panels (used for feed-in-tariff), and one that measures heat pump consumption (which was a surprise of the installation, I think it was fitted for a subsidy that doesn't currently exist).

When the panels are backfeeding the main meter just puts a red LED on and stops counting. The solar installation is hardwired, not a balcony one.

initially yes but then the local power supplier will come and install a bidirectional meter