They bond very well with their owners. I’ve had three males, two currently (caged separately). In general, they are very sassy and want to be part of everything! They have a big parrot personality. They are extremely intelligent and love investigating what you’re up to. They are also very sweet and cuddly. I hand tamed Milo myself and he has become quite the attention hog. He likes to sit on my hand and stare at me while I sweet talk him lol. Luka would live glued to my hand for constant cuddling if it was an option. But they can also be independent as long as you give them things to do. I have a playstand for them to hang out on while they’re out of the cage. That way they can still spend time with me if I’m doing something else. I’ve never had issues with teaching mine not to bite.
As for your budgies, they should be very closely supervised. Parrotlets are 50/50 on getting along with others (even other parrotlets). So you’ll have to be careful with any out time together. You should decide first if you’re okay with giving them separate out times if they don’t get along at all. It is a very real possibility. My current two, Milo and Luka, have to have separate out times.
Fun story of parrotlet sass
Last month, Milo and I were hanging out on the couch. He went over to my hand, leaned down to bite, stopped short, and then said “no bite no bite!”. And repeat. He teased me for like 10 minutes pretending like he was gonna bite. The little bugger
Another time he was getting scratches and I brought him closer to snuggle against my cheek. As I brought him closer, he pulled up one foot and gently tapped my face twice like “Listen, human. I love you and all that, but a bird needs space.” I pulled him away from my face and he went right back to asking for scratches