Yes, that is certainly possible! We have a lot of experience with clients travelling to foreign countries. We make sure that the certificate is internationally accepted and has a QR code to validate its authenticity with your camera app.
You are responsible for checking the test requirements of your destination.

Your booking confirmation number, ID, and don't forget your mask! Be aware it is not possible to get tested with only a copy of your ID.

Validated rapid tests administered by a qualified healthcare professional. The medical and pharmaceutical responsibility of the testing rests with the employed physicians and pharmacists of the testing provider. This is basically a nasal swab. The test provider may choose to combine the nasal swab with a throat swab. For PCR tests are ISO 15189 certified laboratories used.

Yes, that's possible. PCR tests are very good at detecting the virus in the period prior to becoming ill, so they are more reliable before you have symptoms. If you decide to take an Antigen Test without complaints, it may be negative, in which case the result has no value, or it may be positive and in that case you should assume that this is correct. It is therefore better to do the PCR test to exclude an infection without symptoms.