Is the total mass of the universe decreasing? Nuclear fusion leads to conversion of a small amount of mass in to energy. However, no (or a few) physical phenomenon appears to convert energy into mass.
As we have so many stars with large scale fusion occurring at the core. Is the net mass of the universe decreasing?

I found a relevant note on black holes, which says:

As per Hawking: The matter is converted to energy and some of the energy gets converted to equal amounts of matter and antimatter, the matter goes out of the black hole, but the antimatter goes inside the black hole and in turn decreases its mass. Ultimately after millions or even billions of years, the black hole will be evaporated away. completely. So that means every matter that goes into the black hole is responsible for its destruction.

 A: Dealing with the example of an isolated star. During its life, nuclear fusion ultimately results in radiation from the photosphere that carries energy into space. As a result the mass of the star must decrease, because the total mass-energy is conserved.
However, another property that is conserved is the baryon number (the total number of protons and neutrons). How is this number conserved yet the mass decreases? The answer is that the baryons get together as more massive nuclei with negative binding energy.
If we now look at a co-moving volume in the universe (that is a box that expands in proportion to the universe as a whole), then more and more hydrogen and helium is fused into heavier elements which reduces the amount of mass in the form of atoms and nuclei. However this is partially made up for by the radiated energy (divided by $c^2$) in the form of photons and neutrinos which is in the box.
I say partially, because stellar remnants like neutron stars and white dwarfs have negative gravitational binding energy that reduces their gravitational mass.
All this pales into utter insignificance compared to other cosmological phenomena going on in the box. The radiation energy density decreases as the scale factor to the power four, so the co-moving radiation energy decreases with the scale factor. The radiation energy density is however much smaller than the matter density (at any epoch when stars can form), which in turn is smaller than the energy density of the vacuum (aka dark energy). The vacuum energy density appears to be constant. This means that the vacuum energy in a co-moving volume increases as the cube of the scale factor.
So to sum up, what is commonly referred to as "mass" will decrease (slightly), but the total mass/energy appears to be increasing roughly as the cube of the scale factor.
A: 
Is the total mass of the universe decreasing?

No. Of course, I can't prove that, but I can say that we know of no example wherein energy is not conserved. Conservation of energy applies to every situation we know. Energy can neither be created nor destroyed. Apply this tenet to the universe along with the mass of a body is a measure of its energy-content, and the answer to the question is no. 

Nuclear fusion leads to conversion of a small amount of mass in to energy. However, no (or a few) physical phenomenon appears to convert energy into mass.

Radiation converts a small amount of mass into energy. This is why Einstein said "if a body gives off the energy L in the form of radiation, its mass diminishes by L/c²". This body could be a burning log. There is no law of conservation of mass. Note though that if you contain the energy, you have to account for its mass-equivalence. See https://arxiv.org/abs/1508.06478 by van der Mark and (not the Nobel) 't Hooft. If you catch a photon in a mirror-box, it increases the mass of that system. The mass of the burning log reduces a little, but the radiation from the burning log contributes to the mass of the universe, which doesn't change. 

As we have so many stars with large scale fusion occurring at the core. Is the net mass of the universe decreasing?

No, the mass of the stars is decreasing. If you had a burning log in a mirror-box on a pair of scales, the reading on the scale does not decrease.  

I found a relevant note on black holes, which says: As per Hawking: The matter is converted to energy and some of the energy gets converted to equal amounts of matter and antimatter, the matter goes out of the black hole, but the antimatter goes inside the black hole and in turn decreases its mass. 

This is nonsense I'm afraid. Antimatter does not have a negative mass. We know of no particles that have a negative mass or negative energy. 

Ultimately after millions or even billions of years, the black hole will be evaporated away. completely. So that means every matter that goes into the black hole is responsible for its destruction.

I'm afraid Hawking radiation remains hypothetical. And even if the black hole did evaporate, conservation of energy still applies. That energy is still in the universe with its mass-equivalence, so the mass of the universe doesn't change. 
Note that some people will tell you that dark energy is continually being created, which would mean the mass of the universe is increasing. However this is hypothetical too.
