Preparing Time Series Data for LSTMs

I have no formal education here but my understanding is that RNNs take an input window and “unfold it”, basing each prediction in part on those prior. Say I have a batch size of 1: There shouldn’t be a relationship between the first batch and second, correct? (if not, tell me; the rest is irrelevant)

Does it follow from my understanding that it’s safe to

• Have overlapping windows in my data? (so conceptually, have batches 0, 1, 2 = data[0:4, 1:5, 2: 6])
• Split into fit/val sets derived from random choices of windows? (rather than just slicing twice)
• Shuffle data after windowing?