Yes. She can.
Accepting probation is like making a deal with the Devil. It keeps you out of jail but it places you at the whim of your PO and the mercy of the (oftentimes unmerciful) State.
You are free to file a motion with the Court seeking to clarify (and the Court may even agree with you and "stand down" your PO), but remember that your PO has the power of the pen (a mere allegation, sans any proof, may not be enough to cause permanent damage but is certainly enough to put a damper in your day) so you are always going to be best served by accepting your situation and complying with your PO's requests (unreasonable or complicated as they may be).
It is not uncommon for PO's start tough / strong and, once they see compliance and a lack of resistance then they lighten up. I suggest that you grin and bear it for a few weeks and see if she does not lighten up. If not then consider hiring a lawyer to speak to her and to file a motion, but this should be your last resort.
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Yes she can require you to report weekly. However you may file a motion with the court to request that it be specified that you are to report once a month and no more.
Yes she can
This is not intended to be legal advise or as legal representation. I am a California personal injury attorney . Be aware that every state has its own statute of limitations; and statutes & case laws that govern the handling of these matters.
Unfortunately, the answer is yes. However, you may want to petition the court to address the hardship of traveling to the PO's office in order to obtain a more reasonable time frame to submit the work log.