How often does the light come on? Mine (I've got an '06 1.2 8v) used to come on only if I'd gone into full lock one way or the other. Turning the engine off and back on would clear it, since I've put a new alternator and battery on I've not had the light come on at all.
For checking the battery, do it with the ignition off first, the battery should be showing between 12.4v and 12.6v, anything under that shows the battery isn't fully charged or is not holding a charge properly
Now turn the engine on, the reading should now be around 14.5v (although I think the minumum is 13.8), if it's higher than 14.6 it can damage the battery.
So.... a good battery should be showing about 12.5v with the engine off and then with the engine on the alternator should be pumping out about 14.5v.
My daughter had an '02 punto a few years back, I used the guides to change the steering column and got a refurb unit from BBA-Reman off Ebay (they're in Rochester, Kent).
Make sure you get the info off the sticker on the motor as there are two types.
If you have the tools it isn't a hugely difficult job, I did it on my drive in about 2.5 hours.
https://www.ebay.co.uk/itm/Fiat-Pun...epair-Service-Lifetime-Warranty-/391718692644
Here are the guides, I know it says HGT but it worked perfectly for my 1.2 8v
Guide Part One:
https://www.fiatforum.com/punto-mk2...eplace-pas-column-punto-mk2-hgt-part-1-a.html
Guide Part Two:
https://www.fiatforum.com/punto-mk2...eplace-pas-column-punto-mk2-hgt-part-2-a.html