Notice that the above answers will include DateTime, TimeStamp, Category and other datatypes.

Using object is more restrictive (although I am not sure if other dtypes would also of object dtype):

1. Create the dataframe:

   df = pd.DataFrame({
       'a': ['a','b','c','d'], 
       'b': [1, 'b', 'c', 2], 
       'c': [np.nan, 2, 3, 4], 
       'd': ['A', 'B', 'B', 'A'], 
       'e': pd.to_datetime('today')})
   df['d'] = df['d'].astype('category')
   

That will look like this:

   a  b    c  d          e
0  a  1  NaN  A 2018-05-17
1  b  b  2.0  B 2018-05-17
2  c  c  3.0  B 2018-05-17
3  d  2  4.0  A 2018-05-17

2. You can check the types calling dtypes:

   df.dtypes
   
   a            object
   b            object
   c           float64
   d          category
   e    datetime64[ns]
   dtype: object
   

3. You can list the strings columns using the items() method and filtering by object:

   > [ col  for col, dt in df.dtypes.items() if dt == object]
   ['a', 'b']
   

4. Or you can use select_dtypes to display a dataframe with only the strings:

   df.select_dtypes(include=[object])
      a  b
   0  a  1
   1  b  b
   2  c  c
   3  d  2
   

Yes, its possible. You use dtype

import pandas as pd
import numpy as np

df = pd.DataFrame({'a': ['a','b','c','d']})
if df['a'].dtype != np.number:
    print('yes')
else:
    print('no')

You can also select your columns by dtype using select_dtypes

df_subset = df.select_dtypes(exclude=[np.number])
# Now apply you can label encode your df_subset

4 years since the creation of this question and I believe there's still not a definitive answer.

I don't think strings were ever considered as a first class citizen in Pandas (even >= 1.0.0). As an example:

import pandas as pd
import datetime

df = pd.DataFrame({
    'str': ['a', 'b', 'c', None],
    'hete': [1, 2.0, datetime.datetime.utcnow(), None]
})

string_series = df['str']
print(string_series.dtype)
print(pd.api.types.is_string_dtype(string_series.dtype))

heterogenous_series = df['hete']
print(heterogenous_series.dtype)
print(pd.api.types.is_string_dtype(heterogenous_series.dtype))

prints

object
True
object
True

so although hete does not contain any explicit strings, it is considered as a string series.

After reading the documentation, I think the only way to make sure a series contains only strings is:

def is_string_series(s : pd.Series):
    if isinstance(s.dtype, pd.StringDtype):
        # The series was explicitly created as a string series (Pandas>=1.0.0)
        return True
    elif s.dtype == 'object':
        # Object series, check each value
        return all((v is None) or isinstance(v, str) for v in s)
    else:
        return False