Yes, the datacenter proxies (Premium & Dedicated) are static and do not change. This means that they stay the same for the duration of your subscription.
No, the Residential proxies are rotating by default and will change with each new connection you make. However, you can use a static session to maintain the same IP for a period of time — there is no strict limit on session length, but we recommend a maximum of 120 minutes. With the Unlimited Residential plan, sticky sessions can run for up to 12 hours (43,200 seconds). Note that the IP may rotate before the session expires if the peer providing it goes offline.