Birds don't tend to like hugs. As prey species, being hugged feels too much like being caught by a predator. As parrots, touch on the back, belly, over the wings, under the wings and vent (basically everywhere that isn't their head) is reserved for mates only. If you stroke your parrot's back, the parrot is going to assume that you're in a relationship. This sounds cute but many, many parrots lose their home because of it. Most species of parrot are intensely monogamous (with some rare exceptions) so this can cause tensions between you and other people. Your intensely monogamous parrot is NOT going to be impressed if you hug your family members or cuddle your partner! A parrot will either attack a potential rival for your affections, or nip and bite their partner to drive them away from a potential rival. This is interpreted in a pet context as "aggression".
It is important to never let your parrot believe you are mates in the first place, even though it means you are more restricted in where and how you can touch them.
Interact with and include in daily life? Sure. Many parrots want to be included in flock activities and will be upset if they can hear stuff going on that they aren't involved in. Mine "helps" me wash up. Yesterday we dealt with a pile of junk mail - the humans sorted it and ripped addresses off envelopes and letters, we gave those to Leia, and and she shredded those into teeny bits of paper. You can use clicker training to teach a parrot tricks like targeting a stick, turning around, opening their wings and so on - this will also help you learn how to communicate with each other.