If you're spending a few days in Andorra

Yes.
The Andorran, Spanish and French authorities have taken no measures to close the borders and movement into the country. The Government of Andorra is therefore currently applying no restrictions on entering the country, nor on the movement of people and vehicles around its territory.

SPAIN*
Citizens and residents of Spain are free to move around Andorra.
Before traveling, find out about the current measures.

FRANCE**
Citizens and residents of France are free to move around Andorra.
Before traveling, find out about the current measures.

OTHER DESTINATIONS
You may enter Andorra unrestricted from any stop-over destination, but should bear in mind that additional health-related documentation may be requested depending on your country of origin. 
Please see DO I HAVE TO PROVIDE ANY HEALTH CERTIFICATE IN ANDORRA?

Check for updates at the following links:
Information website for Spain and Catalonia.
Information website for France.

No.

No.

Except in health and social care centers, where it is still mandatory.

Any tourist or visitor who needs to have a TMA or RAT COVID-19 diagnostic test can request one at the Government STOP-LAB equipped for this purpose. Phone: (+376) 821 955.

Many of nationally-certified private clinical analysis laboratories perform PCR and RAT diagnostic tests.

LIST OF LABORATORIES PROVIDING PCR / TMA / RAT TEST

LIST OF PHARMACIES PROVIDING RAPID ANTIGEN TESTING (RAT)

No. They will not have to pass any form of health check. You will only need to bring their pet health passport, as per the usual requirements.