What is carbanion? Please explain with mechanisms along with the respective bond fission? Thank you :)

Carbanions, and enolates, are relied upon for carbon-carbon bond formation in synthesis; in general, the negative charge can be delocalized onto a heteratom to offer stabilization. The classic means of carbanion formation are via the diesters of malonic acid, #HO_2C-CH_2CO_2H#:

#RO_2C-CH_2CO_2RrightleftharpoonsRO_2C-CH=C(OH)R#

The neutral enol is stabilized by hydrogen-bonding around a 6-membered ring, and the enolic hydrogen can be deprotonated by base to give the enolate, which is an ambident nucleophile:

#RO_2C-CH=C(O^-)RrightleftharpoonsRO_2C-(H)C^(-)-C(=O)R#

This anion tends to react via the carbon centre (rather than by the oxygen) and it is still the standard methodology for #C-C# bond formation.

Lithium reagents are oligomers of the form #(R)_4^(-)Li_4^(+)#, which can react as #R^(-)# nucleophiles (of course they are also used as very strong bases).

Anyway, if I were you, I would look up the relevant chapter of your organic chemistry text; there will be a chapter entitled #"carbanions and enolates"# where this chemistry is precisely discussed.