I think part of your confusion is about which types of variables a chi-squared can compare. Wikipedia says the following about this:
It tests a null hypothesis stating that the frequency distribution of certain events observed in a sample is consistent with a particular theoretical distribution.
Thus it compares frequency distributions, also known as counts, also known as non-negative numbers. The different frequency distributions are defined by the categorical variable; i.e. for each of the values of a categorical variable there needs to be a frequency distribution that can be compared to the other ones.
There are several ways to get the frequency distribution. It might be from a second categorical variable wherein the co-occurances with the first categorical variable are counted to get a discrete frequency distribution. Another option is to use a (multiple) numerical variable for different values of a categorical variable, it can (e.g.) sum the values of the numerical variable. In fact, if categorical variables are binarised the former is a specific version of the later.
Example
As an example look at these sets of variables:
x = ['mouse', 'cat', 'mouse', 'cat']
z = ['wild', 'domesticated', 'domesticated', 'domesticated']
The categorical variables x and y can be compared by counting the co-occurances, and this is what happens with a chi-squared test:
'mouse' 'cat'
'wild' 1 0
'domesticated' 1 2
However, you can also binarise the values of 'x' and get the following variables:
x1 = [1, 0, 1, 0]
x2 = [0, 1, 0, 1]
z = ['wild', 'domesticated', 'domesticated', 'domesticated']
Counting the values is now equal to summing the values that correspond to the value of z.
x1 x2
'wild' 1 0
'domesticated' 1 2
As you can see a single categorical variable (x) or multiple numerical variables (x1 and x2) are equally represented by in the contingency table. Thus chi-squared tests can be applied on a categorical variable (the label in sklearn) combined with another categorical variable or multiple numerical variables (the features in sklearn).
Best Answer
Assuming you are in the context of stepwise regression, the scale of the feature does not matter. The F-test is done on the difference of RSS values between the smaller and larger model as calculated on the outcome variable (also taking into to account the difference in the number of parameters).
For more information see: http://en.wikipedia.org/wiki/F-test#Regression_problems