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Why do lens don't splits light into its seven constituent colors, like Prism?
Lenses do split light just like prism do. In fact a lens is effectively built up out of tiny prisms. The splitting of the light is known as chromatic aberration.
The lens in your camera is a compound lens that is designed to (mostly) remove the chromatic abberation by using combinations of simple lenses. For example the simplest such lens is an achromatic doublet.
Why do lens don't splits light ... like Prism?
Generally they do in the real world. It is called chromatic aberration.
into its seven constituent colors
The constituents of visible light is a continuum not seven distinct colours. The way we linguistically label ranges of frequencies is arbitrary and varies across cultures.
Why is lens left is correct, not right one?
It's an idealisation. Some materials and some designs of lenses, or compound lenses, produce less chromatic aberration. Sometimes we use the concept of ideal things to explore more basic concepts at a simple level (e.g. refraction)
How does lens came to know that rays are coming from infinity or are at Focus and converge/diverge them at different point accordingly?
a) Lenses don't know things. b) This can be explained by simple laws of refraction.
Real lenses suffer from chromatic aberration due to the refractive index of glass varying with the wavelength of light.
All a lens does is to refract incoming rays of light.
It so happens that if rays of light close to and parallel to the principal axis of a lens cross at a point after refraction.
This dispersion curve from Wikipedia Commons shows how the index of refraction varies with wavelength. It is this dispersion property which results in the splitting of light into a variety of colors, as observed in prism demonstrations and rainbows.
We see that if Dense Flint is used for a lens, there will be quite a bit of color splitting. With the crown glasses, there is less, and in this graph, the dispersion (as well as the visible-range indices of refraction) are smallest for fluorite.
High quality fluorite lenses are prized by photographers for their very low chromatic aberration. They are also very expensive, with a 70-200 mm zoom going for US$1200.
Regarding your 2nd question, the focal point is defined to be the location at which paraxial rays converge.
All the other answers that lenses do show chromatic aberration are perfectly true, but usually they do not show it to anything like the same degree as a prism. This it's because prisms are typically operated with light at much higher incidence angles to their interfaces than for lenses. For an incidence angle of $\theta$, the refraction or angular deviation wrought by the interface is, from Snell's law:
$$\Delta\theta=\arcsin\left(\frac{n_2}{n_1}\sin\theta\right)-\theta$$
So that a change in that deviation owing to a wavelength induced refractive index shift is:
$$\mathrm{d}_{r_n} \Delta\theta =\frac{\sin\theta}{\sqrt{1-r_n^2\,\sin^2\theta}}$$
Where $r_n=n_2/n_1$ and this quantity increases with incidence angle, especially if total internal reflexion is approached.
At least one of the incidence angles in a prism is of the order of $45^\circ$; one seldom allows an angle anything like as high as this in lens design. The reason for this is that spherical aberration is roughly caused by the nonlinearity in Snell's law; if Snell's law were $\theta_1/\theta_2=n_2/n_1$, then spherical lenses would truly focus rays to a point.
Whenever one has severe refraction in lens design, one adds a great deal of aberration which must be nulled elsewhere in the lens system; one thus tends to end up with finely balanced differences of large aberrations and the design becomes exquisitely sensitive to the positioning of lens elements. Thus one only ever sees it in applications where high optical powers in few surfaces are needed and the cost justifies someone's hand tweaking of lenses as the system is built. Typically in miniaturized, high cost optics like microscope objectives.
As John Rennie says, the stacking of different materials can compensate for chromatic aberration. A spherical surface with different materials either side will be converging at wavelengths where the refractive index on the side of the center of curvature is greater than the other, diverging at wavelengths when this side's index is the lesser of the two and the surface yields no power at the wavelength where the two indices are equal. Thus one can choose such surfaces to offset the wavelength dependent optical power elsewhere in the system. "Achromatic"systems bring two wavelengths to a common focus ( usually at either end of the visible spectrum) , apochromats bring three wavelengths to a common focus and I have in the past designed a system bringing seven wavelengths to a common focus. Needless to say, that was a highly specialized application.
