Actually the murky water thing is not true. Although Bettas can live in muddy water because they are anabantids (meaning they breath air) they do best in clean, filtered and warm (around 80 degrees F) water.
One of the reasons that Betta's don't live as long in captivity as they could/should is because people have been given the mistaken information that Betta's should be kept in small bowls. This is not true, they shouldn't be kept in anything smaller than a 10 gln. tank although if well kept some do Ok in 5 gln. tanks. IMO it's cruel for stores to sell them in those small plastic cups, also leaving people with the impression that they can live in those or a small bowl. For us, when we moved our male Betta from his 10 gln. to a 30 gln. and then to our 55 gln. tank he became much more 'alive' with each move. He truly seemed happier with the larger tank space - we could literally see it in his personality.
Also, as stated, you shouldn't ever have two males within sight of each other and never in the same tank. Although people think they kill each other in the wild that's not true. The loser of the fight runs (well, swims) away from the winner. In a tank setting the loser cannot get away and thus, will often be killed as the more aggressive/winner will continue the fight since their is no safe retreat for the loser.
Male Betta's should never be kept with other fish that have long flowing fins (Angelfish, Gouramis, etc.) as that usually leads to fights as the Betta sees the other fish as a competitor. They can live very peacefully with other types of fish.
If you have a male with females you should have at least three females so the male doesn't harass just one but spreads out his 'advances' between them thus giving the females a break from his attention.
You new fish looks beautiful. Hope some of the above is helpful .... fish are a wonderful hobby.