Python and data analytics how to get the unique number of orders per seller using groupby?
Based on the information available above I think the solution below should work

# Number of unique orders per seller
a = pd.pivot_table(df, index = ['seller_id'], values = ['order_id'],
                   aggfunc = {'order_id' : pd.Series.nunique})

# Products that are being ordered the most per seller
# Products that are being ordered the most in general
b = pd.pivot_table(df, index = ['seller_id', 'name'], values = ['product_id'],
                   aggfunc = 'count')

# Sum of the quantity field for each product to check how many times has been order
c = pd.pivot_table(df, index = ['name'], values = ['product_id', 'quantity'],
                   aggfunc = {'product_id': 'count', 'quantity': 'sum'})

# Number of orders for each customer
d = pd.crosstab(df.customer_id, df.order_id)