If I delete the contact app for more data. Will I lose all my contacts?

According to this, the contacts will remain in the phone app.

Delete built-in Apple apps on your iOS 12, iOS 13, or iPadOS device or Apple Watch - Apple Support

If you delete the Contacts app, all of your contact information will remain in the Phone app.

However, the app takes up very little space and there are bigger uses of storage than the contacts app. Photos and videos can be real storage hogs.

I have no idea how the data in the phone app would interact with the contacts app if you install it again. If you are syncing contacts with iCloud, I imagine that the contacts would download to your phone again after reinstalling the app.

Contacts shouldn't be lost, as they are automatically synced with www.icloud.com. After you click the link, just sign in to your Apple ID and click the Contacts icon. However, deleting the contact app won't do much help to you.

Yes, unless they are set to sync to iCloud. The Contact app uses very little storage, so deleting it will not recover much space.