Sending a group email using Gmail

No, this is the design of the Gmail app. Given the problems I've read about with using Gmail in the native Mail app on the iPhone, I've not tried it that way, although I know of others that have. You can create groups for Contacts in iCloud, but I'm not sure that Gmail app would have access to them.

You can download the Gmail app for the iPhone and sync your contacts from there if you wish.

Do you have a name for these groups? If you type that group name in, what happens. When you check in the settings for the Gmail app, does it show anything for contacts? I don't have any groups in my Gmail contacts, because it is only used for receiving junk mail. Test your account and see if it will bring up the group names.