difference between scaling/normalizing data at a specific step

Question

I am using the MinMaxScaler normalization method, however I have seen various ways that this can be done, I want to know if there is any actual difference between the following:

1. Standardizing/Normalizing the data before splitting the data into train and test

Code 1

scaler = MinMaxScaler() #Normalization
#Transform X and Y values with scaler
x = scaler.fit_transform(x)
y = y.reshape(-1,1)
y = scaler.fit_transform(y)

# Split Data in train and validation
x_train, x_valid, y_train, y_valid = train_test_split(x, y, test_size = 0.25)

2. Standardizing/Normalizing the data after splitting the data into train and test and then scaling on train and test

# Split Data in train and validation
x_train, x_valid, y_train, y_valid = train_test_split(x, y, test_size = 0.25)
  
# created scaler
scaler = MinMaxScaler() #Normalization

# transform training dataset
x_train = scaler.fit_transform(x_train)
# transform test dataset
x_valid = scaler.fit_transform(x_valid)

3. Standardizing/Normalizing the data after splitting the data into train and test. Then fitting on the training set and then scaling on both train and test

# Split Data in train and validation
x_train, x_valid, y_train, y_valid = train_test_split(x, y, test_size = 0.25)
  
# created scaler
scaler = MinMaxScaler() #Normalization
# fit scaler on training data
scaler = MinMaxScaler().fit(x_train)

# transform training dataset
x_train = scaler.fit_transform(x_train)
# transform test dataset
x_valid = scaler.fit_transform(x_valid)

Answer 1

Case I -
With a single scaling step, you might leak the test info into the train. In this approach you have a common min/max otherwise it would have been two pairs See, the plot for one of the Features of Iris dataset
Also, we don't scale the target. But I see this in your code.

Case II -
This is fine but you should also consider the online cases, where you will not have a test set to scale the new test data.

Case III -
This is a better and an agnostic approach.
Your code implementation incorrect as suggested in the comment