Probation is a period where the court imposes so could keep an eye on people who are convicted of a crime. Yes you street at all time, and yes you can talk to cops and be like a normal person. What you are required to do is to "Obey All Laws" and not to be arrested again. If you do, you are potentially looking at jail time. But if you don't until your probation is over, then you will be fine.
My colleague is correct. If you are interested the word probation comes from Latin through old French and means a period of time in which you have to prove yourself. In CA we have two kinds of probation: formal probation where you have to report regularly to adult probation, pay fines and fees etc and informal probation (more properly called a conditional sentence) which is none reporting. Failure to follow the conditions of either form of probation can result in a jail or prison term.
The terms of your probation should have been specified by the court. Since you were charged with trespass, I imagine that you received "informal probation" (see my colleague's answer for the difference between this and "formal" probation). Since you trespassed, there's a good chance that part of the probationary sentence includes your staying away from the area that you trespassed.
If you don't know what the conditions of probation are, you should reach out to your attorney (the PD) and get him to look in the court file or look at the minutes (the recorded notes of what happened in court) and have him remind you.
The information provided in this answer is for general information only – such information is NOT legal advice for any case, investigation, or any other legal matter. Reading, receiving, or conveying the information in this answer does not create an attorney-client relationship.