Using old sim

You should not have any issues, as long as the new iPhone is unlocked, or if locked is locked to the carrier you are using now.

The tariff you are using is part of your service plan, and does not get chnanged by inserting the sim card into another phone.

In most cases it will be unlocked yes. From the U.S store:

What phone do you currently own? The iPhone 11 supports the Nano SIM technology, it's very likely your old phone also used a Nano-SIM. The Nano SIM has been the current standard in iPhones since 2012.