Will it be okay for me to go to the beach/swim in the sea one week after my microdermabrasion treatment?

The only concern when going to the beach one week post-treatment would be prolonged exposure to UV rays. Take all of the standard precautions such as sunblock, a wide brimmed hat, and sunglasses and you should be fine.

Microdermabrasion is a very superficial treatment of the skin. The skin usually heals within a few days after treatment. It is recommended to avoid the sun or use sun block for the first few days after microdermabrasion. You should be able to enjoy the beach or similar activities one week after treatment. 
Remember, always use sun block to avoid skin cancer. But as far as your microdermabrasion treatment is concerned, one week is plenty of time for your skin to completely heal.
Good Luck!

Use plenty of sunscreen and you should be fine, especially a week later. For future reference, wait at least 1-2 days afer a microdermabrasion treatment before exposing your face to UV rays.