The author said - I want to set up I-cloud mail on my new Mac air M2 but my Apple ID is my gmail account.
They are setting up a new Mac , in initial stages third party mail services like gmail , yahoo mail address is required to sign in with as an Apple ID , the mail address say example2@icloud.com can't be created directly from Mac .
However when Apple ID say example1@gmail.com is signed in Mac , further they can create new Apple ID say example2@icloud.com from web , alias of iCloud address is created when Apple ID say example2@icloud.com is signed in Mac system preferences , account recovery is done for 2FA accounts when the password and account credentials are lost .
In new Mac secondary authentication account is created initially in which three answers for respective questions , date of birth , rescue mail address and its password are added , further its a choice to add trusted numbers and verify them and convert the account into 2FA .
The author also said - will getting an i-cloud email address change my Apple ID?
No , once Apple ID say example1@gmail.com is signed in Mac , it will remain signed in , the second Apple ID say exammple2@icloud.com can be created from Mac , but this will be a simple mail address unless its switched and signed in Mac , simultaneously credentials for primary Apple ID ( say example1@gmail.com ) are used to create it .
Lastly they wrote -
also my gmail account is connected to all my professional communications and web urls like web ex Microsoft etc., I want to keep that gmail address as my primary email can I do this and still use I-cloud email address?
They want Microsoft , that is again to be downloaded in new Mac , the new iCloud mail address say example2 @iCloud.com can be added in Mac system presences > internet accounts .