Check both, the key existence and its length:

import json, sys

obj=json.load(sys.stdin)

if not 'results' in obj or len(obj['results']) == 0:
    exit(0)
else:
    exit(1)

You're misunderstanding how in works. in checks to see if a key exists in a dictionary, it does not index into a dictionary. That's what the square brackets do.

if 'title_jpn' in json_data['gmetadata'][0] is not "":

The above line will not evaluate as you expect. It should be.

if json_data['gmetadata'][0]['title_jpn'] is not "":

This can be further simplified because empty strings '' always evaluate to False in python. So instead of checking if the string is not empty, just check if it has any value at all like the following:

if json_data['gmetadata'][0]['title_jpn']:

If you're trying to guard against the fact that title_jpn might be optional and not always exist, you need to do two conditions in your if statement (which I think is what you were originally trying to do):

if 'title_jpn' in json_data['gmetadata'][0] and json_data['gmetadata'][0]['title_jpn']:

The above line first checks if the title_jpn key is present before trying to check if it's value is empty. This can be further simplified using the dictionary .get() method which allows you to supply a default.

if json_data['gmetadata'][0].get('title_jpn', None):

The above will check if title_jpn is in the dictionary and return the value if it does, or None as a default if it does not. Since None is interpreted as False in python, the if block will not run, which is the desired behaviour.

dict.get(key, default=None)

However, since .get() automatically sets the default value to None, you can simply do the following.

if json_data['gmetadata'][0].get('title_jpn'):

You have to use os.path.getsize(path) to find file size of a file.
You do not have to read file at all.
If JSON file is just 2 bytes, "[]" or "{}", it is an empty JSON object.

Based on some JSON usage principles, in this particular case it is sane and safe to presume that a 2 bytes long JSON string is an empty string, array or object ("", [], {}). A two digits number may be a valid JSON string but it is not what JSON is used for (you can use JSON library to load a single value like you can use a big crane to lift an egg).

If this [file size] does not fulfill your requirements you have to read the first 2 bytes and check if they are equal to '[]':

with open(filename, 'rb') as file:
    if file.read(2) != '[]':
        file.seek(0)  # it may be redundant but it does not hurt
        json.load(file)

"example" in data.keys() will return True or False, so this would be one way to check.

So, given JSON like this...

  { "example": { "title": "example title"}}

And given code to load the file like this...

import json

with open('example.json') as f:

    data = json.load(f)

The following code would return True or False:

x = "example" in data   # x set to True
y = "cheese" in data    # y set to False

You don't need the intricate tests on wether 'text' is present for the post caption. This code works well with the JSON string you posted:

for post in data['data']:
    if post.get('caption'):
        print post['caption'].get('text', 0)

Furthermore, you could be more defensive and refer to data.get('data', []) when starting the loop in case Instagram sends you empty JSON.

If the list of "emailAddresses" is empty, the for loop doesn't get executed. Accordingly print("boo") neither.

You need to check the list first, before iterate through the list:

results = response.json()["data"]
for item in results:
    emails = item["contacts"]["emailAddresses"]
    if emails:
        for email in emails:
            print(email)
    else:
        print("boo")

You can use any(), returning True if any of the values in the JSON object are truthy:

Copydata = {
  'a': [],
  'b': [],
  'c': [1,2,3]
}

result = any(item for item in data.values())

print(result)

This outputs:

CopyTrue