Yes. Sure, especially with your mommy and daddy. Babies own us...Or so they think. We are theirs, and they want us to give them our full attention. And, they don't want anyone coming between or interfering with that. Soothing reassurance will help, but it will take awhile for them to mature and understand that they can "share" you.
Yes. Most babies and toddlers exhibit jealousy, especially when a parent holds or pays attention to another baby. They are starting to learn how to express what they like and don't like!