Using iMAC as bigger screen with MacBook Pro

If you're talking about Target Display Mode, the answer is no. New Macs don't support using any iMac as a Target Display – including iMacs that have that feature.

Use your iMac as a display with target display mode - Apple Support

If you're talking about AirPlay to Mac, your iMac might be able to act as an AirPlay Receiver if Apple introduced it in 2019 or later, and it is running Monterey or later. Note that AirPlay is not the same as a first-class hardware monitor connection, and there may be limitations with respect to resolution, lags, and/or artifacts.

System requirements for Continuity features on Apple devices - Apple Support

Set up your Mac to be an AirPlay Receiver - Apple Support

No.

Depends. What version of MacOS is your iMac running? You may be able to connect your new MacBook Pro with your old iMac if you have the latest MacOS and have Sidecar enabled.

Also they need to follow the requirements below:

• Both devices should be upgraded to at least MacOS Monterey.
• Both devices must be signed in with the same Apple ID using two-factor authentication. Sidecar does not support Managed Apple IDs.
• To use Sidecar wirelessly, both devices must be within 10 meters (30 feet) of each other and have Bluetooth and Wi-Fi turned on.