Rare dragons are certainly less likely to be bred when they're an option. It's all a matter of chance, though there's been some unproven theories that the dragon you put on the left side of the breeding menu determines the order of elements of the egg. It doesn't seem to hold true.
Generally assume the breed will yield a random possible combination, and note that rare dragons are very rare, I'd say maybe less than a 10% chance. I don't think there's any formal numbers. From experience only Rare dragons have a different breeding chance, everything else, assume an even chance of all other possible results. If there is a difference, it's not large enough to fuss over.
Special Event dragons also tend to be "Rare" at approximately the same rate as the Sun/Moon/Rainbow dragons. Generally you'll want to stop everything and start trying to breed time-limited dragons immediately until you get one, or two if you want a breeding pair.
Note the Epic Breeding Island advertises that you have a higher chance of rares. It doesn't seem extremely significant; rare dragons are still rare on the breeding island. In fact I haven't noticed a perceptible difference, but if you're trying to breed for rares you might as well try the island first.
Also note that breeding two dragons always gives you that same dragon (best I can tell), so breeding two Rare Rainbow dragons has a 100% chance of giving a rainbow dragon.
Decorations definately improve visitors, but paths add tons of them at a low cost.
Vistitors really freaking like paths.
Before I filled that island with paths I had 90 visitors. Decorations will cost you way more and get you maybe a visitor or two per object. Buy decorations because you want, not because they add visitors.
Note that there are many other ways to get visitors, they're not just from decorations.
Also don't put much stock in the specific suggestion the Vistiors button gives you, it appears to be random; you can get the "More Islands" tip when you have the maximum amount of islands for example.
Also, apparently the visitor boost you get from building all these paths is temporary. After installing all of these paths visitors eventually decline down to what they were before you built the paths.
Generally, don't even worry about visitors; the number does not impact your cash flow. You earn cash because of your dragon's earn rate even if you have 0 visitors; it's magic.
Visitors are a fun way to see "how well" your park is doing but they're a rough metric with no in-game benefit whatsoever.
Best Answer
The counter goes up when you purchase one, just like Buildings, so it's a limit on how many you can purchase. From the wiki article on the Vernal Fountain it sounds like the game lags if you have too many of these items (they're animated) so they limit you to prevent you from crashing the game.
I own one of these and I can confirm it doesn't give a boost to Bloom dragons at all and appears perfectly decorative. None of the other decorations have in-game benefits either (other than raising the meaningless Visitors counter) so this seems normal.