Ok,
for your info, I relaunched it with a t2.small as advised and will tell you if it works.
As for Heroku, I tried a hobby tier with a postgress hobby feature.
Seems to work ok, some communications failure though, we’ll see if the pulse do work.
Moreover, I already contacted AWS’ support and they are going to tell me what plan is the most relevant for running metabase at a smaller cost.
It seems that via cloudwatch it is possible to schedule up and down time for metabase instance: eg: let it run during the day only or when pulse are scheduled.
I will keep you posted.
Matth