How can I prevent a user to use admin rights to work around restrictions? We just bought my husband a new Mac. 
Currently, we each have parental restrictions requiring a password on our accounts when it comes to "mature" ratings on our iPhones and iPads (older generations) This holds us accountable for each other and prevents inappropriate "adult" material from being viewed:downloaded on our machines and causing issues in our marriage. 
However, with the new MacBook Air that we purchased, he is the administrator because it is his computer. We noticed you can't set up parental controls as the administrator. Is this correct? 

If he were to set up another account as a guest, could he still use his iCloud under that setting? Could we lock the administrator account so that settings could not be changed? 
Could someone set the password for "administrator" to something we don't know and have him use an account as a managed user under his Mac? 

What is the best way to own the computer, be the primary user but also set self limitations?
Well, somebody (aka at least one user account) needs to have full admin privileges on a Mac, there is no way around it. If you want to restrict the ability of an account, you will have to set up a dedicated user account (and define Parental Restrictions for it) and use this account for day to day work.

You would still need an admin account to install software etc, so you could for instance split the admin password in half, with each of you only knowing one part. Whenever an admin password is required, you both would need to sit in front of the Mac then and enter your respective half.