multiple if else conditions in pandas dataframe and derive multiple columns

Here is a way to use numpy.select() for doing this with neat code, scalable and faster:

conditions = [
    (df2['trigger1'] <= df2['score']) & (df2['score'] < df2['trigger2']) & (df2['height'] < 8),
    (df2['trigger2'] <= df2['score']) & (df2['score'] < df2['trigger3']) & (df2['height'] < 8),
    (df2['trigger3'] <= df2['score']) & (df2['height'] < 8),
    (df2['height'] > 8)
]

choices = ['Red','Yellow','Orange', np.nan]
df['Flag1'] = np.select(conditions, choices, default=np.nan)

you can use also apply with a custom function on axis 1 like this :

def color_selector(x):
    if (x['trigger1'] <= x['score'] < x['trigger2']) and (x['height'] < 8):
        return 'Red'
    elif (x['trigger2'] <= x['score'] < x['trigger3']) and (x['height'] < 8):
        return 'Yellow'
    elif (x['trigger3'] <= x['score']) and (x['height'] < 8):
        return 'Orange'
    elif (x['height'] > 8):
        return ''
df2 = df2.assign(flag=df2.apply(color_selector, axis=1))

you will get something like this :

You need chained comparison using upper and lower bound

def flag_df(df):
    
    if (df['trigger1'] <= df['score'] < df['trigger2']) and (df['height'] < 8):
        return 'Red'
    elif (df['trigger2'] <= df['score'] < df['trigger3']) and (df['height'] < 8):
        return 'Yellow'
    elif (df['trigger3'] <= df['score']) and (df['height'] < 8):
        return 'Orange'
    elif (df['height'] > 8):
        return np.nan
    
df2['Flag'] = df2.apply(flag_df, axis = 1)

    student score   height  trigger1    trigger2    trigger3    Flag
0   A       100     7       84          99          114         Yellow
1   B       96      4       95          110         125         Red
2   C       80      9       15          30          45          NaN
3   D       105     5       78          93          108         Yellow
4   E       156     3       16          31          46          Orange

Note: You can do this with a very nested np.where but I prefer to apply a function for multiple if-else

Edit: answering @Cecilia's questions

1. what is the returned object is not strings but some calculations, for example, for the first condition, we want to return df['height']*2

Not sure what you tried but you can return a derived value instead of string using

def flag_df(df):

    if (df['trigger1'] <= df['score'] < df['trigger2']) and (df['height'] < 8):
        return df['height']*2
    elif (df['trigger2'] <= df['score'] < df['trigger3']) and (df['height'] < 8):
        return df['height']*3
    elif (df['trigger3'] <= df['score']) and (df['height'] < 8):
        return df['height']*4
    elif (df['height'] > 8):
        return np.nan

2. what if there are 'NaN' values in osome columns and I want to use df['xxx'] is None as a condition, the code seems like not working

Again not sure what code did you try but using pandas isnull would do the trick

def flag_df(df):

    if pd.isnull(df['height']):
        return df['height']
    elif (df['trigger1'] <= df['score'] < df['trigger2']) and (df['height'] < 8):
        return df['height']*2
    elif (df['trigger2'] <= df['score'] < df['trigger3']) and (df['height'] < 8):
        return df['height']*3
    elif (df['trigger3'] <= df['score']) and (df['height'] < 8):
        return df['height']*4
    elif (df['height'] > 8):
        return np.nan