Low scale ML/statistical techniques for data poor settings
Generally, I'd pick a very simple, transparent/explainable model and use the results in a semi-automated way. That is, do not just derive a prediction but rather insights. You could, for example, use a (or multiple) decision tree(s) which you pre or post prune. The result could be a tree with, let's say, just 1-3 features to find simple rules like &quot;if a customer is married and at least X years old, they have a high chance of making a purchase&quot;. With logistic regression you may use coefficients to identify features which influence the dependent variable the most. These (qualitative or semi-quantitative) rules should then be validated with domain experts.
Moreover, you need to be transparent about the accuracy and precision of your estimates. In the above example, leave purity would provide some intuition. If you report any quantitative measures (which I'd be careful with), you may want to consider confidence intervals (see here or chapter 5 in Tom Mitchell's &quot;Machine Learning&quot;, for example). (With only 10 samples typical assumptions about normal distribution will not hold here though)
Regarding the time series I would start even simpler. Depending on the number of customers, I'd start by visualizing some or all historical data in a line plot (sales per customer over time) and check the min, max and mean per customer. This gives some intuition regarding potential trends. For example, if all observations remain constant over time for a given customer, whether there is an upward/downward trend or if the data has high variance with no clear trend. Also, there may be clusters of customers which show similar patterns. Obviously, this is neither Machine Learning nor a rigorous statistical analysis but rather a pragmatic approach supported by some basic data analytics.
What you need to be very careful with is the time horizon of any quantitative prediction: based on 10 observations at $t \in \{1,21,...,201\}$ you may derive some conclusions for, let's say, $t&lt;=301$ (to make up a total out of the blue ballpark figure) but $t=621$  is very far in the future. Also, you need to keep seasonality in mind. For example: If your observations are all from October to April of a given year and assuming you have a winter/summer seasonal pattern. Then you cannot infer a lot for months May to September. To understand the limitations and forecast potential of your time series better, I'd speak to subject matter experts, e.g. in sales &amp; marketing. It could also be helpful to understand their forecasting approach and cross check any insights you derive with their predictions.
But, as Erwan pointed out, be very careful to derive conclusions. Applying some &quot;ML magic&quot; will not find a useful pattern if there insufficient data to find any signal. And of course additional data collection would be reasonable if that is an option.