First of all relax and breathe......
Typically once your lender orders the appraisal, it should be back in a week or two at most. Typically you would not have control over when it was ordered or when it is returned. So waiting weeks....not sure where that comes into play. I don't think that is a reflection on the appraiser. Could be, but that would be somewhat unusual. If there is a concern, ask your lender when it was ordered.
How long did you have between contract and closing? Typical is about 30-60 days. Most lenders seem to want to jump right on the appraisal, but not all do nor is it needed. They know their processing times.
The appraisal is more than just visiting the house....sometimes the appraiser does most of the work before visiting, sometimes after, so turn around times after the visit can vary. Could be a couple of days...could be a week. So nothing unusual there to me.
It is not unusual for the seller's agent and even the buyer's agent to never see or talk to the appraiser or see the appraisal or know the number. Possible....nothing wrong with it, but many appraisers don't have time to be out calling and negotiating with people. If they needed questions clarified they might call. There are reasons they could call or could need clarification.
In the end I am not sure of what your concern is unless you have contracted on a house based on the appraised value. That is unusual.
Let's say your contract is for $200,000.....you agreed on this, your agent discussed the CMA with you, other properties you saw were in this price range.....and the sellers and the appraiser somehow conspire to get the appraisal to $250,000. Your contract would still be at $200,000, so why would you care? How are you damaged?
The only time I can think this would really be an issue is if you thought the property was worth X and the seller thought it was worth Y and you came up with some kind of agreement to let an appraiser decide the value and you would purchase at whatever the price the appraiser came up with. That would be unusual.
I would suggest you discuss your concerns with your realtor in a calm fashion.
The appraiser is not prohibited from speaking with the seller, or the seller's agent. Think about it, they have to call someone to get inside the house.
In the end I'm thinking if you contracted on a house for $200K and the appraisal comes back at $250K, you would be happy and think you got a great deal.