For proof of stay, you might want to see this thread: 14-Day Requirements: Proofs.
Portugal aims to apply the EU rules regarding border checks and stamping of passports - outlined here: https://ec.europa.eu/transparency/documents-register/api/files/C(2019)7131_1/de00000000092844?rendition=false. See Section 1 for border check rules, and Section 6.2 sub-section (i) for stamping of passports. In principle, no entry or exit stamp must be affixed “to the travel documents of nationals of third countries who present a residence card provided for in Directive 2004/38/EC.)”
There are, of course, instances where the passport has been stamped despite a non-EU national having a valid EU residence card. During the past 2 years this has happened frequently to UK nationals holding an EU residency card (and some without a card but with a residency certificate or QR code (eg Portugal)). The EU has consequently clarified as follows: Stamping a passport serves to establish whether a non–EU national respected the authorised length of a short stay within the Schengen area, but … the usual limitation of a stay of 90 days in a 180 days’ period in the Schengen area does not apply to [the EU country where a non-EU national has a residency card] irrespective of whether their passport has been stamped or not.
In relation to whether Schengen travel is allowed and duration of stay limits for non-EU nationals with an EU residence card the rules state that "A long stay visa or a residence permit issued by a Schengen State allows you to travel or stay in other Schengen States, while respecting the maximum duration of a “short stay” (a stay of “90 days in any 180 day period”). See question 16 in FAQs at: https://imigrante.sef.pt/wp-content/uploads/FAQsFronteiras_EN.pdf