Two sources of light having same frequency and zero or constant, intial phase difference are called coherent sources.

Fringe width \(\beta =\cfrac { D\lambda }{ d } \Rightarrow \beta =\lambda \) for same D and d. When the whole apparatus is immersed in a transparent liquid of refractive index n = 4/3, the wavelength decreases to \({ \lambda }^{ ' }=\cfrac { \lambda }{ n } =\cfrac { \lambda }{ 4/3 } \) width decreases to \(\cfrac { 3 }{ 4 } \) times.

Yes, since magnification depends upon the focal length and focal length depends on the color and different colours have different wavelengths (i.e., different refractive indices.)
\(\cfrac { 1 }{ f } =\left( \mu -1 \right) \left( \cfrac { 1 }{ { R }_{ 1 } } -\cfrac { 1 }{ { R }_{ 2 } } \right) \) 
(By Lens Makers Formula) Also, magnification of the compound microscope
\(M=\cfrac { -L }{ { f }_{ o } } \left( 1+\cfrac { D }{ { f }_{ e } } \right) \)

For relaxed eye, L = f₀ + f_e.
for least distance of distinct vision
L' = f₀ + u_e, u_e e
Therefore, L' < L, that is, the distance will be decreased.

(i) Fringe width of interference fringes, is given by \(\beta =\cfrac { D\lambda }{ d } \propto \cfrac { 1 }{ d } \) . If the sources are far apart, d is large; so fringe width (β) will be so small that the fringes are not resolved and they do not appear separate.
(ii) That is why the interference pattern is not detected for large separation of coherent sources.