How to extract particular key from the dict()?
You could iterate over all the keys and apply function1 to them and them append to the full_data_set. At the end you have all them concatenated. 

However, Python lists are unordered, so you don't control the order which keys are chosen.

data = {
    'aaa': [1, 0, 6, 8, 0, 5, 9, 1, 1, 0],
    'abc': [1, 1, 1, 2, 4, 0, 0, 0, 9, 8],
    'cfg': [0, 0, 0, 4, 3, 1, 0, 0, 0, 1],
    'cghjj': [7, 8, 9, 2, 3, 0, 0, 0, 0, 0]
}

def function1(l: list):
    # do something
    return l

full_data_set = []

for key in data.keys():
    full_data_set += function1(data[key])


If you do want to control the order of the keys, you need to make the ordered list of the keys somehow.

key_order = ['aaa', 'abc', 'cfg', 'cghjj']

data = {
    'aaa': [1, 0, 6, 8, 0, 5, 9, 1, 1, 0],
    'abc': [1, 1, 1, 2, 4, 0, 0, 0, 9, 8],
    'cfg': [0, 0, 0, 4, 3, 1, 0, 0, 0, 1],
    'cghjj': [7, 8, 9, 2, 3, 0, 0, 0, 0, 0]
}

def function1(l: list):
    # do something
    return l

full_data_set = []

for key in key_order:
    full_data_set += function1(data[key])