Predicting future order dates and order amounts for customers with online retail data
To answer your points in order:


I can generally understand what you are trying to do. However, a few considerations you should bear in mind:

1.1. Given that you are trying to make time series predictions for all customers, then you are most likely interested in a panel data modelling solution - i.e. one that takes into account the fact that the data is both cross-sectional (at one point in time) and time series (across several time periods). The alternative is simply running a separate time series for each customer, which could prove to be highly inefficient.

1.2. This would be considered a multivariate time series forecast - provided that price is in fact dependent on variables other than itself, i.e. quantity, country, etc. Are you planning on incorporating these as explanatory variables into a time series model?
Hard to say how many models should be used off the bat, but I might be inclined to construct a single panel data model for this case - you could always construct it on a subset of the data as a proof of concept and then work from there. Construction of multiple LSTM models would appear too much effort for too little reward (in terms of forecast accuracy).
I would be inclined to take a look at linearmodels - it is a Python library designed for working with panel data.
These techniques are used for representing categorical data - you might find the following answer useful.


Hope this helps, and please let me know if I can offer any further clarity on the above.