"I need to have a table with a column with the sourcetype name, a column linked to the first column in order to have all the sources for a specific sourcetype and a last column with the count of events by source...."
Your original attempt was close, but you need to combine both into 1 stats command, like this:
index="x"
| stats count values(source) by sourcetype
Edit: Just realized I read your requirement wrong. You need the count by source, not by sourcetype, so above would not really work. But your requirements are then conflicting. You want the count by sourcetype,source, but for some reason have a problem with repeating the sourcetype value for each related source.
This should do the trick:
| stats count by source,sourcetype
| stats list(source) as source list(count) as count by sourcetype
