First of all, from the looks of that video, I think your budgie is clipped. A little hard to tell with it being far away. You can figure it out yourself from the following images:
Clipped Budgie:

UnClipped Budgie:

Note the black primaries sticking out behind the wings and almost running to the tail.
As for jumping back to the cage, the best thing to do is make the cage disappear when the budgie is out. Either put it in another room, cover it, put it in a box, whatever so the Budgie doesn't know it's around. Most of the bigger parrots really prefer being out but Budgies tend to like their cages. They can overcome this through learning but not as long as it keeps going back to the cage.
Here's another issue, cage has food, water, and toys. What does your out of cage perch have? Diddly. Look into getting a playgym (for budgies they have really cheap ones like $20). Put some toys on it, water bowl, food bowl. Down the line when you want to do training lose the food/water bowls from there so it isn't munching all day but for now it's a good way of providing a desirable alternative to the cage. When it learns there is food there, it will want to hang out there more. Then you stop putting food there but it will still like the place not remembering why it liked it.
For touching, first off understand that Budgies are more handsoffish. They don't really like being pet by people. Your finger is huge to them, it's like you're running your fist through your hair. So understand that it may never actually get anything desirable out of it. That said, you can tame it using millet. Look at my
toweling and
taming articles on the
trainedparrot blog. You'll see techniques that can be applied similarly without a towel but just your hand instead.
Finally, in the future, even if you explain things in a video, write out your questions in the forum post or it's hard to discuss for people who don't/can't watch the video and it makes it harder to remember everything you asked. Very tame budgie you have there though, much easier than ones I've dealt with.