Sleeping in dorms / hostels
Relating dorms specifically in Warsaw I can't answer but I have stayed in all kind of dorms and never had any trouble. Of course you hear stories and strange things really happen. I remember a guy once, in the next room, whose belongings were stolen. This was classified as a safe hostel by the reviews.
In the end it's up to you and your practices. You are in a shared space with unknown people. You should either carry or secure your most valuable belongings (ID, Passports, etc. included). In principle no one is going to steal a bag of dirty laundry but if you walk around showing your latest iWhatever, etc. someone might actually think it's worth it to break or take your bag/lock. In general the more valuable things you leave unattended/show off the biggest is the risk. Mitigation is up to you.
Side note about hostels: Locks are not always safe. Some are very easy to break. In some hostels you are allowed to leave your most valued goods at the reception.
Security in Warsaw
I was there this year. It's a perfectly normal city. It felt very safe even at night. At least around the center where I spent most of the time. I was staying in the suburbs and even during the commute in public transport, by night, it seemed fine.
Again, common sense is the most important thing here. Don't put yourself in strange places / situations and you should be safe.