Use df.sample() to get samples of data frm a dataframe:
a = np.arange(1,81).reshape(8,10)
df = pd.DataFrame(a)
df1= df.sample(frac=.25)
>>df1
    0   1   2   3   4   5   6   7   8   9
5   51  52  53  54  55  56  57  58  59  60
3   31  32  33  34  35  36  37  38  39  40
For a random permutation np.random.permutation():
df.iloc[np.random.permutation(len(df))].head(2)
    0   1   2   3   4   5   6   7   8   9
6   61  62  63  64  65  66  67  68  69  70
1   11  12  13  14  15  16  17  18  19  20
EDIT : To get 20 elements in a list use:
import itertools
list(itertools.chain.from_iterable(df.sample(frac=.25).values))
#[71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
frac=.25 means 25% of the data, since you have used 80 elements 25% gives you 20 elements, you can adjust the fraction depending on you many elements you have and how many you want.
EDIT1: Further to your edit in the question: print(df.values) gives you an array:
[[ 1  2  3  4  5  6  7  8  9 10]
 [11 12 13 14 15 16 17 18 19 20]
 [21 22 23 24 25 26 27 28 29 30]
 [31 32 33 34 35 36 37 38 39 40]
 [41 42 43 44 45 46 47 48 49 50]
 [51 52 53 54 55 56 57 58 59 60]
 [61 62 63 64 65 66 67 68 69 70]
 [71 72 73 74 75 76 77 78 79 80]]
You would require to shuffle this array using np.random.shuffle , in this case , do it on df.T.values since you also want to shuffle columns:
np.random.shuffle(df.T.values)
Then do a reshape:
df1 = pd.DataFrame(np.reshape(df.values,(4,20)))
>>df1
    0   1   2   3   4   5   6   7   8   9   10  11  12  13  14  15  16  17  18  19
0   4   3   10  2   8   7   1   5   6   9   14  13  20  12  18  17  11  15  16  19
1   24  23  30  22  28  27  21  25  26  29  34  33  40  32  38  37  31  35  36  39
2   44  43  50  42  48  47  41  45  46  49  54  53  60  52  58  57  51  55  56  59
3   64  63  70  62  68  67  61  65  66  69  74  73  80  72  78  77  71  75  76  79