How can I fix joint between shoulder strap and chest strap?

I tend to repair all straps using metal rivets, a rivet gun and washers. Better than sewing. You can prepare a hole in the nylon strap by carefully heating a small nail in a flame from your camping stove, held in pliers, and pushing it gently through.

Don't mess with the clip (unless to replace it entirely). Compress the piping (cord) so that is narrow enough to slide the clip on. Usually you only need to get one end/corner of the clip on and then the clip will keep the piping compressed while you slide the rest on.

Doing it towards one end (away from wherever you normally put the strap) is best since the piping may stay a little squished and you don't want to make it easier for the clip to come off. Also, the piping is usually a little tapered/compressed by sewing towards one end, so the clip may slide on there naturally anyway.

Usually you can just use your fingers to squeeze the piping, but if it's difficult try using pliers--the part right next to the edge of the pliers will also be compressed, and you can put the corner of the clip on there.

Press one corner of the clip against the bead (tube, piping, whatever it's called). Slide the clip smoothly down the bead while pressing firmly inward. The jaws of the clip should "ride up" the bead, spreading them apart and around. Once one corner is in place, keep sliding it smoothly down while pressing, like pulling a zipper, and the rest should follow.

This will do less damage to the clip than prying it apart, and you should be able to do it repeatedly without damage. If it came off this easily once, you'll probably need to do it repeatedly.

The best option is to change the clips. You can buy a new one starting at 1$, that's not expensive. You can try to repair it using a strap, but if you have an opportunity and you are not camping with it now, that's a bad idea. If you repair it, it will break another time, and we don't know when. If you don't want to have it broken while camping it's better to change it now. You can do that in atelier or manual by yourself.

One solution, if you don't need the strap to be adjustable along the piping (vertically), is to remove the plastic clip and sew the chest strap to the shoulder strap, in the right place for you.

Any sewing machine can do that, or you can do it by hand if you don't have a machine accessible.

Those clips do come off, and in many designs you'd be able to thread them back on from the end. It is possible to clip them back on though.

The way I've found works is to gently prise open one end of the slot by twisting a screwdriver in it. Then slide that end over the piping, so that the piping replaces the screwdriver in the slot. The rest of the slot will go fairly easily.

Try to avoid doing this too often - if it keeps going you might be over-tightenting the chest strap, or snagging it on things.

It's also possible to replace the strap with one that wraps round the shoulder straps, though on that pack it wouldn't stay in place without further fastening