Is my mortgage process time frame normal?

I am purchasing a house. The day under contract is 5/4, loan application submitted on 5/6 evening, rate lock 5/10, I am using a mortgage company, which my agent recommended. Most time the communication is between my agent and mortgage company. So far the bank doesn’t order the appraisal yet, the agent said she had pushed mortgage company really hard. I don’t understand why it’s take so long to lock a mortgage rate (the interest rate increased 0.125% from 5/6 to 5/10) and I don’t understand why the appraisal is not done yet. Is the time frame in my case sounds normal?The seller wants closing in 30 days, I am worried if we can get this done on time. Any suggestion will be appreciated.
Thank you

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