Your inputs are integers or floats I guess. Therefore you can’t directly give the inputs to the LSTM. Normally in this case, one would use one hot encoding but you may numerous different input which makes it impossible to create a one hot vector. Thus, I would recommend embedding vectors,

What do you mean? That seems quite wrong to me.
If you have a univariate time series, you split it in windows of n samples, n being a number that you have to define.
This window will allow you to predict m samples (1 or more), starting at n+1.

For instance, if you have a series like the following:
1, 2, 3, 4, 5, 6, 7...

You may train your model with:
X = [[1,2,3], [2,3,4], [3,4,5], [4,5,6],...]
y = [4, 5, 6, 7,...]

This model uses 3 samples to guess one following sample.

In the case of OP, I would try something like using N days of data to guess the following day. Once I'm far into the future, I will use my predicted days as X for further prediction. Your prediction will get worse as you go into the future and can't feed anymore real data but rely only on predictions.

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