I have both first and second year ladies.
I only have one who is in her third year and I can't tell the eggs apart so I don't know how well she is specifically laying. :)
No, the gene that causes blue and splash is the same.
If the chicken has two genes for black then it's black.
If it has one gene for black and one for blue then it's blue.
If it has two genes for blue then it's splash.
It might have made more sense if they'd named the gene splash instead of...
Yes.
The statistics don't work out for small numbers, but over enough eggs hatched, for every 100 chicks Blue x Blue will give you 25 Black, 50 Blue, and 25 Splash.
It took me about 30 chicks to get my first splash and then the next hatch had a disproportionate number of them. :D