Your LimeSurvey account lives at account.limesurvey.org, separate from your survey site. It holds the survey site itself, your login, your plan and your invoices. Only the primary admin of a plan logs in here. See Overview: The primary admin account.
Log in at account.limesurvey.org. From your survey site, click your name at the top right and then Membership & billing.
The page Your account has four tabs. The menu behind your name at the top right of account.limesurvey.org opens the same pages and has Logout.
The first tab has three blocks:
Below them, ComfortUpdate Features sells update keys for self-hosted Community Edition installations. LimeSurvey Cloud doesn't need them.
See Manage your account and survey site.
See Billing, payment and invoices.
At sign-up, yes: your survey site starts with the same username and password as your account at account.limesurvey.org. After that they are separate, and changing one doesn't change the other. See Can't log in? Reset your password or recover your account.
On the Account details tab under Remaining responses, and on your survey site in the top bar: point at the number to see Response balance. See How responses are counted and what happens at your limit.
Click Upgrade at the top right of your survey site. See Upgrade your plan.