On the size of some stars being one tenth the size of the Moon, I guess it can be reworded better that it is in reference to the visible apparent diameter of some stars being one tenth the visible disk of the Moon.
I don't know which stars that sort of statement might refer to Tom, but with the exception of the Sun, we cannot see the physical disks of any other stars without resorting to specialist techniques possible only at the worlds largest observatories. For example I believe the VLT can be used to detect the physical disk of Betelgeuse with all of the main 8.2m telescopes working in unison as an interferometer.
The Sun itself of course has a visible disk equal in size to that of the Moon. So which stars have a size one tenth that of the Moon? I have been studying astronomy for a looonnngg time and I have never come across that suggestion. Modern astronomers both amateur and professional would laugh at such a claim.
The universe has been tranparent to light (all types of EMR in fact) since about 300,000 years after the Big Bang. That is the moment when the Universe cooled down enough to allow neutral atoms to form. Before that the elementary particles that formed during the primordial nucleosynthsis period created a kind of fog which interacted with photons making their mean free path about centimeter or less. After neutral atoms formed at the epoch of Recombination the Universe became transparent to light and so photons could traverse the Universe unhindered.
So now light can travel for unlimited distances across the Universe. Quasars can be seen across billions of light years across space and I have personally imaged galaxies using my home observatory equipment which are almost a billion light years away. The size of stars is irrelevant. It is the amount of energy (light) they are emitting that decides how far across space they can be seen from. You may be aware of the so-called 'holes' in the milky way which are actually clouds of cold, dark hydrogen (part of the ISM). The molecular hydrogen making these clouds have larger diameters than the wavelength of optical light and so the light from stars behind these clouds is absorbed. The astronomer E.E Barnard catalogued many of them which is why the Horsehead Nebula for example is listed as Barnard 33.
I agree some stars are considered to be large. Extremely large. We can determine that from studies of the light they are emitting. As I stated before we can easily measure luminosities and temperature using both spectral analysis and by comparing their brightness at two distinct wavelengths (colour index). So we don't need to see their physical disk size to know they are big.
I don't understand why flat Earth theorist don't seem to acknowledge the progress of astronomy made since about the middle of the 19th century. I agree that more progress has been made in astrophysics and cosmology during the last century to 150 years than ever before. There have been some ideas and hypotheses that have led us to dead ends but others have brought us new and exciting knowledge. That is the same with everything in life. It seems to be only the former that FE people seem to acknowledge. Less than 25 years ago we had not discovered any planets beyond our own solar system. Now thanks to the Kepler spaceprobe we know they are common place. It is surely only a matter of time before we discover another 'Earth'; a planet supporting life (but not necessarily humanoid of course). I'm not so excited about that prospect though I have to say. I will continue to love studying the Universe whether there is life elsewhere in it or not.