There are lots of questions here, let's take them one at a time.
Are star getting less massive as a result of nuclear fusion?
Yes. If a star has a luminosity $L$ then this corresponds to a mass change $c^2 dM/dt$.
For the Sun $L = 3.83\times10^{26}$ W, so the Sun is getting less massive at a rate of 4 million tonnes per second. However, over the Sun's main sequence lifetime of $10^{10}$ years, this amounts to a decrease of only $6.7\times 10^{-4}$ solar masses. Later stages of nuclear burning result in a more luminous Sun, but these phases are also much shorter, so the overall effect on the Sun's mass is similar.
In contrast, the solar wind has a mass loss rate of $\sim 2 \times 10^{-14}$ $M_{\odot}$/yr (but may have been much stronger in the past). This means that the mass lost in a wind and the mass lost by nuclear fusion are comparable over the main sequence lifetime. However, in later stages of the Sun's life it will lose some tenths of a solar mass during the red giant and asymptotic giant branch phases due to a radiatively driven dusty wind.
Something similar is true for most stars: averaged over their lives the mass lost in nuclear fusion is negligible compared to the mass loss they experience as a result of direct loss from stellar winds, and is also a very small fraction (less than 0.1%) of the original mass of the star.
Are stars getting less massive on average with time
Possibly, but it is very difficult to tell. When we look at old populations of stars then they do not contain massive stars because they have lived their lives and died. But I guess what you mean is whether the mass spectrum at star birth is shifted towards lower masses?
There is certainly theoretical evidence that the earliest metal-poor stars could be built to have very high masses - the so-called population III stars. Once metals are present in the gas then radiation pressure due to the gas opacity prevents the construction of very massive ($>200 M_{\odot}$) stars.
Further down the mass spectrum the evidence for any variations in the so-called "Initial mass function" with time is weak or absent. The conclusion of a big review by Bastian, Covey & Meyer (2010) is that there is no evidence for any variation "over cosmic time".
Are stars getting more metal rich?
Yes. All elements heavier than He (bar traces of Li and Be) are mostly produced inside stars (or perhaps in neutron star mergers for a lot of the heavier elements). Therefore the stellar "ecological cycle" of birth and death results in an overall increase in the metal-richness of the interstellar medium and hence the stars that are then produced. To understand exactly the rate at which this occurs requires a complex "galactic chemical evolution model".
It turns out that most of the increase in metallicity (in our Galaxy) occurred very early on - between 8 and 12 billion years ago; when the star formation rate was much higher and the rate of production of massive stars and supernovae was probably an order of magnitude higher than it is now. As a result, the rate of increase of metallicity now is much smaller. The 4.5 billion year old Sun has a similar metallicity to stars that are being produced in the solar neighbourhood right now.
Let's also put this into context. Even after about 12 billion years of star formation and stellar death, the metallicity of the interstellar medium still only consists of order 2% by mass of elements heavier than helium.
Do more metal-rich star die younger?
No, it's the other way around but lifetime is not hugely sensitive to metallicity. At a fixed mass one can show that the luminosity on the main sequence relates to metal mass fraction $Z$, as $L \propto Z^{-1/6}$. i.e. High metallicity stars have a lower luminosity than more metal-poor stars of the same mass, but the dependence is weak. As the fuel supply is dominated by hydrogen, and as a mass fraction this is very similar in both metal-rich and metal-poor stars, then the lifetimes of metal-rich stars are longer. e.g. see Figs 1 and 2 of this paper by Bazan & Mathews (1990) - Fig.2 shows that The physical reason here is that lower metallicity stars have lower opacities in their outer enevelopes and this makes them smaller and hotter at the same luminosity. A smaller star at a given mass has a hotter interior and this speeds up the nuclear processes slightly and makes the star more luminous.
