Julie,
I'm not in Italy at the moment, but a few comments on the No. 2 trails.....
You can check the current status on the official C.T. parks website (it seems to be updated on a regular basis) - http://www.parconazionale5terre.it/sentieri_parco.asp?id_lingue=1
It appears that all of the trails are currently closed, but it's likely that at least some will be re-opening by about April 1st which is the start of tourist season (depending on their state of repair at the time). It's quite common for one or more of the trails to be closed at various times during the year if they sustain damage from storms or whatever.
The Via dell' Amore (Riomaggiore-Manarola) was closed about 25 Sept. 2012, following a severe rock slide which seriously injured four Australian tourists, and it's been closed since that time. It's expected to re-open this year, but no specific date has been mentioned AFAIK.
At least some of the No. 2 trails should be open during your visit.