Mmm. The problem is that it mostly LOOKS shady. I'm sure your friend and her family are all very nice and responsible people in need, but what if your friend was someone else and they were buying TVs with the donations?
Listen, I appreciate your caring for your friend, but this isn't going to be very effective most likely. It's not that we're mean, it's that we'd like to know where our money actually goes. When I donate, I donate to charities that I know are going to use the money well. My suggestion is that instead, you put your efforts into finding local assistance.
I know when my mom had breast cancer she found out about all kinds of help. One really simple, but useful one was incredibly-healthy, home-cooked food delivery during her recovery process. If I were you I'd contact local charities that might be able to set you up in a way that you could fund-raise in a more usual manner.