Re: The sun is losing mass?
Yes, the article is really confused. The Sun loses about 4 million tonnes a second from fusion (ie it turns about 4 million tonnes of hydrogen a second into light), and about 1.5 million tonnes per second due to the solar wind. So fusion is the dominant process here, although they're of the same order.
Further, what the paper is actually interested in is constraining the gravitational constant, because it's very interesting to know if it's changing obviously. They get a result which has a bound on (dG/dt)/G of the order of 10^-14, which is pretty small.