My question is how N_u units of LSTM works on a data of N_x length? I know that there are many similar questions asked before but the answers are full of contradictions and confusions. Therefore I am trying to clear my doubts by asking specific questions. I am following the simple blog here:
https://colah.github.io/posts/2015-08-Understanding-LSTMs/

Q0) Is keras implementation consistent with the above blog?
Please consider the following code.

import tensorflow as tf
N_u,N_x=1,1
model = tf.keras.Sequential([
    tf.keras.layers.LSTM(N_u, stateful=True, batch_input_shape=(32, 1, N_x))
])
model.summary()

For simplicity, my input data here is just a scalar and I have one time step. The output shape is (32,1). No. of parameter is 12.
Q1) I have one LSTM unit or cell, right? The following represent a cell, right?

I understand from the picture that there would be 12 parameters : forget gate=2 weights+1 bias; input_gate=2*(2 weights+1 bias); output gate=(2 weights+1 bias). So everything is fine up to this point.

Q2) Now let us set N_u,N_x=1,2. I expect the same cell will be applied to the two elements of x. But I found that the total number of parameters now is 16! Why? Is it because I get 4 additional weight parameters corresponding to the LSTM connection between the x_2 and the LSTM unit?

Q3) Now let us set N_u,N_x=2,1. I have now two units of LSTM. Are these two units completely independent or do they influence each other? I expected the parameters number would be 2*12=24, but I in reality got 32 instead. Why 32?

Q4) If I set N_u,N_x=2,2, number of parameter is 40. I think I can get it if I understand the above two points.

Thank you in advance.