Can I back up by connecting my ipad to my iPhone directly?

No, not possible.

Here are Apple’s supported methods of backup for iPad and iPhone:

How to back up your iPhone, iPad and iPod touch – Apple Support

In addition to explicit iTunes and iCloud backup, consider that iCloud already synchronises many types of data between your Apple devices and iCloud.

Beyond these solutions, you can manually backup individual files to external storage devices or other cloud-based services.

No.

A computer or iCloud are the only locations for a backup.