Sounds like you're doing really well! As for your first question, some people will tell you differently, but I am of the opinion that no, you should not do this. This video sums up my feelings on the subject better than I really could:
You're trying to build a relationship with your bird, and doing that will not go smoothly if you're forcing or making him uncomfortable. You want him to associate you with good things. Flock Talk, btw, is an excellent resource, and she has a video all about teaching step up that might be helpful, as well as one about basic parrotlet care.
A contact call is a good sign! It's basically your bird asking, "Where'd you go?" and means he's starting to feel better about you. Try calling back to him to let him know where you are.
Watched the video thanks. We are laying off on the step up.
We made some progress today. He came out on his own three times.
This morning, he came out on his own, and stepped onto my wife arm, and crawled up to her shoulder. The only probem was, we had to get our daughter from school, and he had already been out for awhile and we couldn't get him back into his cage. He runs from our hands, and we didn't want to force him to do anything. We ended up having her lean her shoulder onto the cage area, and then he ran from my hand, jumped on the cage, and ran into the cage to get away from my hand. I have no idea what other option I had, since a treat wasn't working, and after trying for a while we couldn't get him in his cage.
Then....
This afternoon he came out again, while my daughter and wife were at the mall so it was just me. He came out of his cage and went to the ground, walking around. Him and the cockatiel shared some millet withouts getting in a fight. I fed him sunflower seeds from my hand. He got to the point where he would bite the seed directly off my finger. Then he jumped onto my arm. He hung out on my sweatshirt, biting it on and off for a while, and then jumped onto my opposite arm, and climbed to the back of my hand, up to my face and gave a small little bite to my nose, then stared at me super close to my face.
I had him hang out on my shoulder for about 30 mins. A couple times i had to move my hand to nudge him a little because he was biting my neck really hard. My cockatiel does the same thing from time to time, and we just move him off our shoulder if he does that, but I didn't wanna grab Rio or force him onto my finger.
Everything was pretty smooth until I had to put him back. I tried to get him off my shoulder with some millet, but when my hand got too close he flew to the floor. He wouldn't step on my finger, and I think he was full from the sunflower seeds and millet from earlier. Then he stepped on the millet, flew to the couch and hid behind the cushion. I tried to get him to step onto a pencil but he kept biting it. He was running from my hands, and I ended up cornering him and getting him to step onto my hands.
Getting him back in his cage I hope I didn't loose too much ground. I didn't know any other way to do it.
When he went back in he seemed okay, and played with one of the toys. But he is still very wary of me putting my hand in. I had to take my son to baseball, but when I got back I tried to give some millet. He was just as scared of my hand as always.
I really hope I didn't loose too much progress..