You can get divorce even if your husband refuses to sign. Once you proceed with court proceedings, your husband will be asked to appear in court and explain his position.
Yes, you can. This is called a contested divorce. In a contested divorce, you may be forced to go through trial separation. If there are children, you may be ordered into counseling before it goes through.
Yes, if he will not sign the papers go ahead and file. If he does not sign the papers then they will run it in the paper and he will only have so many days to sign or it will be final.