Well it might work, if it’s only a couple of hours. Is it every day you’re using it?
Guessing some numbers
Fan 200 watts/hour
hair dryer fan 50 watts/hour
600 W drill for 10 minutes/hour = 100watts/hour
600 W grinder for 10 minutes/hour= 100watts/hour
So your talking 450W/hour which is 37.5 amps from a 12V battery, but as an inverter is about 80% efficient, it’s more like 47 amps. That’s a pretty major continuous load for a car battery. A 100 A/hr (not CCA) battery would be near enough totally drained over your 2 hour period, which isn’t good for it’s life. I’ve long ago tossed my text books but iirc max discharge of a lead acid battery ought to be to the 70-80% point, so a 100 A/hr battery is only good for say 25 A/hrs, so you’ll need 4 in //. As you’re not Government owned, so there’s no accountability to voters, 2 100A/hr batteries in // ought to give a goodly number of 50% discharge cycles.
As we’re talking about 2 batteries, you might consider a 24V system as the discharge current will be half, which is less hard on the batteries and will keep the terminal voltage a bit higher.
To charge, using a 120W panel, a data book shows a Pmax of 6.74A. To supply 100A/hrs will take well over 15 hours due to charging losses, say 20 hours? To charge a 24V system, 2 60W panels in series will give the same ~20 hours.
It’ll take longer anyway as the panel’s only pointed directly at the sun for a portion of the day.
Now if you’re only in your shed once a week, a smaller panel will work.
A charge controller is needed too.
Or forget the solar panel, and wheelbarrow the batteries back to the house and charge them with a decent multistage charger (bulk, equalise, float).
If your load’s a lot less, then the whole outfit gets smaller of course.
It’s been 25 years since I learned this stuff, so there might be some errors, which I’m sure will be pointed out