Ok it definatly looks like the gasket is gone.
I have a brand new exhaust gasket. I'll sell it half price (€8) plus whatever standard post is. Probably easier to send it by that courier for a €6. Let me know if you want it.
Can't tell from your photo, but the if the link pipe sheared/rotted, maybe you can get a sleeve welded over both pipes.
As for your Cousin....That is a quite normal reaction from your cousin which is why I avoid borrowing bikes and loaning bikes myself....too much at stake like property, money, friendship ect.
But when an owner do allows you to use his bike, then he should already have accepted in his heart and in his pocket (and not just from a fleeting thought in his head), that his bike could be robbed, damaged, returned in an unsatisfactory condition, or written off while in the borrower's possession....and without the possibility of a favourable outcome for the owner. If you are really not willing to accept that....then don't loan.
I am blessed to have two bikes, but I wouldn't allow anyone a loan of one of them no matter how desperate they are. I loaned a bike to a good friend of mine to go to a rally a few years ago. He was desperate to go to this rally with his club. I played the Good Samaritan and even went to the trouble of actually having the bike all spick and span for him for the rally.
When he returned the bike after the weekend, it resembled a motorcross bike that did about 12 hours of non-stop scrambling with all the muck on it. He also managed to damage to fuel filler cap...no problem there, shit happens. But he drove the bike 180 miles home with filler cap open, spewing petrol all over my tank. He wouldn't pay €5 for a universal cap in a garage....sheez!!
Needless to say it left a sour taste in my mouth and in our friendship for a while. But I have to take some of the blame for loaning the bike, and for foolishly placing expectations on other humans which they may fail to live up to.
Just count yourself lucky that your damage is quite fixable. Imagine if the motor blew??.....how would your finances and your relationship with your cousin hold up then???