What is the difference between different batch_sizes in Keras Sequential models?
I need for future prediction using batch_size=1 but affraid of getting bad/wrong result!


Batch size is not connected to the future prediction - it's just the number of samples which will be used in one forward pass to calculate the loss and then in a backward pass to calculate the gradients and parameter updates.

In order to regulate the future prediction (as far as I understand from your question), you just need to define the sample size (or width, or time steps, whatever name you use ...).

Regarding the "important effects of choosing batch_size from 1 to N numbers?" - with a larger batch size your training process might finish faster, but with smaller you might avoid local minimum (but that - local minimum, generally, shouldn't be a problem with deep neural networks).