Group and count total of blanks and total of rows in pandas dataframe

Here's a way to do what your question asks:

df['both_filled'] = (df.Code.notna() & df.Signed.notna()).map({True:True, False:None})
df['Rows_with_any_blank'] = df.Index[df['both_filled'].isna()]
gb = df.groupby('Country', sort=False)
df2 = ( gb.count().assign(
    Rows_with_any_blank=gb['Rows_with_any_blank']
    .agg(lambda x: list(x.dropna().astype(int)))) )
df2 = ( df2.assign(
    Total_Blanks_on_Code=df2.Name - df2.Code,
    Total_Blanks_on_Signed=df2.Name - df2.Signed)
    [df2.both_filled < df2.Name]
    [['Total_Blanks_on_Code','Total_Blanks_on_Signed',
        'both_filled','Name','Rows_with_any_blank']]
    .reset_index()
    .rename(columns={
        'Name':'Total_of_rows_of_the_Country', 
        'both_filled':'Total_of_rows_with_both_values_filled'
    }) )

Input:

  Country   Name  Code Signed  Index
0      CZ  Paulo     3      x      1
1      AE  Paulo   Yes   None      1
2      AE  Paulo   Yes   None      2
3      AE  Paulo     1    Yes      5
4      CZ  Paulo  None   None      6
5      DK  Paulo   Yes   None      9
6      DK  Paulo  None   None     20
7      PT  Paulo     2    Yes     20
8      PT  Paulo     1    Yes     22

Output:

  Country  Total_Blanks_on_Code  Total_Blanks_on_Signed  Total_of_rows_with_both_values_filled  Total_of_rows_of_the_Country Rows_with_any_blank
0      CZ                     1                       1                                      1                             2                 [6]
1      AE                     0                       2                                      1                             3              [1, 2]
2      DK                     1                       2                                      0                             2             [9, 20]

Explanation:

• Create both_filled column which is True if both Code and Signed are non-null and is None otherwise (this allows us to later use count() to effectively sum the number of rows having both columns non-null)
• Create Rows_with_any_blank column which contains the value in Index for rows where neither of Code and Signed is null
• Create a groubpy object gb by Country
• Use count() to get the number of non-null entries per group in each column of gb
• Use assign() to overwrite the Rows_with_any_blank column to be a list of the non-null Index values for each group
• Use assign() to create and populate columns Total_Blanks_on_Code and Total_Blanks_on_Signed
• Keep only rows where the count in both_filled < the count in Name (which is the total number of rows in the original df); this removes any Country for which all Code and Signed rows are filled
• Select the 5 desired columns in the specified order using [[]]
• Use reset_index() to switch Country from the index to a column
• Use rename() to change Name and both_filled to have the specified labels Total_of_rows_of_the_Country and Total_of_rows_with_both_values_filled.

Based on the definitions/conditions you gave, the country AE should have a total blanks on Code equal to 0 and not 2.

Anyway, you can use the code below to get the format of output you're looking for :

out = (df.assign(Total1 = df['Code'].isna(),
                 Total2 = df['Signed?'].isna(),
                 Total3 = ~df['Code'].isna() & ~df['Signed?'].isna())
        .groupby('Country', as_index=False)
        .agg(NumberOfCountries = ('Country','size'),
             Total1 = ('Total1','sum'),
             Total2 = ('Total2','sum'),
             Total3 = ('Total3','sum'))
        ).rename(columns={'Total1': 'Total Blanks on Code', 'Total2': 'Total Blanks on Signed?', 
                    'Total3': 'Total of rows with both values filled', 'NumberOfCountries': 'Total of rows of the Country'})

>>> print(out) :