There are some oddities with the code above, notably that "w" option will overwrite the csv file. from my test this would actually append to an already existing file.

import csv
with open(r'loop.csv','a') as f1: # need "a" and not w to append to a file, if not will overwrite
    writer=csv.writer(f1, delimiter='\t',lineterminator='\n',)
    # two options here, either:
    for i in range(0,10):
       row = [i]
       writer.writerow(row)
    #OR
    writer.writerows([i for i in range(10)]) #note that range(0,10) and range(10) are the same thing

There are two each_dict objects in json_response. They have 5 and 13 tweets, respectively (each_dict['data']). In addition, there are 5 and 13 elements in each_dict['includes']['users'], respectively.

You got 194 elements because in the first iteration of for each_dict in json_response: you save data 5x5=25 times (loop 2 is executed 5 times for every tweet in loop 1). While in the second iteration you save data 13x13=169 times (loop 2 is executed 13 times for every tweet in loop 1).

You should append data to your csv outside loop 2. That is,

for each_dict in json_response:

    for tweet in each_dict['data']:
        # ...
        
        for dic in each_dict['includes']['users']:
            # ...
        
        res = [author_id, created_at, tweet_id, text, bio, image_url]
        csvWriter.writerow(res)

In addition, I recommend using a pandas dataframe to store the info you need and save to csv. It makes the code more readable and you do not have to worry about opening a buffer. See my recommendation below, including renaming:

import pandas as pd

df = pd.DataFrame()

for each_dict in json_response:
    
    for tweet in each_dict['data']:
        row = {}
        row["author_id"] = tweet['author_id']
        row["created_at"] = dateutil.parser.parse(tweet['created_at'])
        row["tweet_id"] = tweet['id']
        row["text"] = tweet['text']
        
        for user in each_dict['includes']['users']:
            if user["id"] == row["author_id"]:
                row["bio"] = user['description']#.encode('utf-16','surrogatepass').decode('utf-16') # uncomment this if you get UnicodeError
        
        for media in each_dict['includes']['media']:
            row['image_url'] = media.get('url', ' ')

        df = df.append(row, ignore_index=True)  
        # Note, since the dataframe is initially empty with no columns, appending a dictionary (i.e, row) will automatically generate the header based on the dictionary's keys.  

df.to_csv('path/to/file.csv')

Output

               tweet_id            author_id                created_at   ...
0   1375057688355336195           2877379617  2021-03-25T12:11:14.000Z   ...
1   1374085719472361474  1265018154444562440  2021-03-22T19:48:59.000Z   ...
...
17  1360693490880032770            926909484  2021-02-13T20:53:03.000Z   ...

As with most file operations you can tell them which way you want to open the file with:

Doku: to_csv

Just use the append mode:

prediction.to_csv("tmp.csv" , sep='\t', encoding='utf-8', \
    doublequote=False, index=False, mode="a")

You might also want to include a

useHeader = True 

before your loop and modify your command to:

prediction.to_csv("tmp.csv" , sep='\t', encoding='utf-8', \
    doublequote=False, index=False, mode="a", header = useHeader)
useHeader = False

so you only get one header on top of the file.

You can do something like this with your for loop:

Declare an empty dataframe at the beginning:

tmp = pd.DataFrame()
for data in url:
    df = pd.read_csv(data)
    tmp = tmp.append(df)
    #df.to_csv(file_name + timestr + '.csv')

# Now, `tmp` will have dataframes for all URL's. You can then write this to `csv

tmp.to_csv(file_name + timestr + '.csv')

Let me know if this is what you want.

The most commonly-used values of mode are 'r' for reading, 'w' for writing (truncating the file if it already exists), and 'a' for appending (which on some Unix systems means that all writes append to the end of the file regardless of the current seek position).

Open the file in append mode:

with open("test.csv","a") as f:
        f.write("name\n")

Check docs here.

Open for reading and appending, store the output then write at the end:

import csv
with open("first.csv","a+") as f:
    r = csv.reader(f)
    wr = csv.writer(f,delimiter="\n")
    result = []
    for line in r:
        # process lines/step 2
        # append to result
    wr.writerow(result)