The COVID-19 tests, when flagged by the SNS (Portuguese NHS), are free of charge for all immigrants, regardless of their situation in the country.

Yes, foreign citizens who don’t hold a residence permit have access to health care under the same terms as the general population.
https://www.sns.gov.pt/sns-saude-mais/cuidados-de-saude-no-estrangeiro-2/

The DINÂMIA-CET project “How to stay at home?” has just released an explanatory manual that graphically clarifies the main measures to be adopted in pandemic times in the different contexts and housing situations.
https://www.cig.gov.pt/2021/03/guia-como-ficar-em-casa-lancado-em-cinco-linguas-estrangeiras-para-apoio-a-migrantes/

Yes, for foreign citizens who wish to have a professional activity as a subordinate or independent worker, and therefore have a relationship with the Social Security system within the scope of a contribution obligation (rights/obligations), they can request the fast track issuing of the Personal Social Number (“NISS na hora”).
http://www.seg-social.pt/noticias/-/asset_publisher/9N8j/content/atribuicao-de-niss-na-hora-a-cidadaos-estrangeiros

In the context of the upcoming local elections, the High Commission for Migrations (ACM), in partnership with the National Election Commission (CNE), released information on the electoral rights and voter registration requirements of immigrant communities living in Portugal.

You can access all the information here: https://www.acm.gov.pt/pt/-/sou-cidadao-estrangeiro-e-resido-em-portugal-posso-votar-nas-eleicoes-portuguesas-

You can contact our team Monday through Friday from 9 a.m. to 5 p.m. using the telephone number or e-mail address provided on our website.

The Águeda CLAIM is open to the public every Tuesday (except on holidays), from 9am to 5pm. The service is available by appointment only.

The CLAIM of Águeda is located in the Business Incubator of Águeda (Incubadora de Empresas de Águeda), and the address is Rua Luís de Camões, n.º 64, on the 1st floor.