Currently the only way to customize your profile picture is to sign in with Google, in which case your profile picture will be updated to the one you have set for your Google account.
A future update to allow you to customize your profile picture without having to sign in to Google is planned.
All (free) accounts are currently limited to 10 typing tests.
A future update to include a premium account with ad-free unlimited data storage is planned.
This means the site is being fixed and/or updated and will be back to fully-functional shortly.
The site will work mostly the same except you will be unable to login and therefore be unable to save data or track your progress.