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.