Reaction:

$Ca(HCO _{3}) _{2} + 2HCl \rightarrow CaCl _{2} + 2H _{2}O + 2CO _{2}$ 

The metal ion displaces the proton $(H^+)$ from the acid and a salt is formed along with carbonic acid $(H _2CO _3)$

Metal carbonates react with acids to give salt, carbon dioxide and water.
$NaHCO _{3} + 2HCl (dil) \rightarrow NaCl + H _{2}O + CO _{2(g)}$.

$CaCO _{3}(s) + 2HCl(aq) \rightarrow CaCl _{2}(aq) + H _{2}O(l) + CO _{2}(g)$ 

Chloride
Hydrochloric acid reacts with Carbonate to form chlorides.
$2HCl+CaCo _3\rightarrow CaCl _2+H _2O+CO _2$

$(A)$  $MgCl _{2}(aq)$ + $CO _{2}(g)$ + $H _{2}O(l)$

When acids react with carbonates, such as calcium carbonate (found in chalk, limestone and marble) a salt, water and carbon dioxide are made. Carbon dioxide is formed as by product which causes bubbling during the reaction and can be detected using limewater.
$Acid + Metal\ carbonate \rightarrow Salt + Water + Carbon\ dioxide$

All carbonates react with acids to produce salt, water and carbon dioxide gas. 
$H _{2}SO _{4} + CuCO _{3} \rightarrow CuSO _{4} + H _{2}O + CO _{2}$

When acids react with carbonates, such as calcium carbonate (found in chalk, limestone and marble), a salt, water and carbon dioxide are made. In general:
$Acid + Metal\ carbonate \rightarrow Salt + Water + Carbon\ dioxide$

Acids give carbon dioxide gas, respective salt and water when they react with metal hydrogen carbonate.
Acid $+$ Metal hydrogen carbonate $\rightarrow$ Salt $+$ Carbon dioxide $+$ Water.

Baking soda and vinegar react with each other because of an acid-base reaction. Baking soda is a bicarbonate $(NaHCO _{3})$ and vinegar is an acetic acid $(HCH _{3}COO)$. One of the products this reaction creates is carbon dioxide. Also Baking soda and vinegar react with each other because they exchange atoms. In this case, they are exchange a proton, which is a subatomic particle that makes atoms.

Sulphuric acid gives calcium sulphate, carbon dioxide gas and water when it reacts with calcium carbonate.
$CaC{O} _{3}   +   {H} _{2}S{O} _{4}   \rightarrow   CaS{O} _{4}   +   C{O} _{2}   +   {H} _{2}O$.

When metal bicarbonates react with acid liberates carbon dioxide The gas evolved because of reaction of acid with metal carbonate or metal hydrogen carbonate turns lime water milky. This shows that the gas is carbon dioxide gas. This happens because of formation of white precipitate of calcium carbonate.
$Ca{\left(OH\right)} _{2}  + C{O} _{2}    \Rightarrow   CaC{O} _{3}  +  {H} _{2}O$.

Acids react with metal hydrogen carbonates and form corresponding salts, carbon dioxide and water. 
Example:
Hydrochloric acid on reaction with sodium bicarbonate forms sodium chloride, carbon dioxide and water.
$HCl  +  NaHC{O} _{3}  \rightarrow   NaCl  +  C{O} _{2}  +  {H} _{2}O$.

Acid rain causes damage to the historical monuments and other buildings. For example Taj Mahal, which is made of marble, is getting damaged because of reaction with acid rain. Marble is calcium carbonate which reacts with the acid and thus gets corroded.

Sodium bicarbonate is also known as sodium hydrogen carbonate, baking soda, baking powder, bread soda and bicarbonate of soda.

Metal carbonate or metal hydrogen carbonate and acid are used in fire extinguisher to produce carbon dioxide gas. Acid and metal carbonate or bicarbonate are kept in separate chambers in a fire extinguisher. On emergency, they are allowed to react with one another. The carbon dioxide gas so produced is poured over fire. As carbon dioxide does not support burning, it puts off the fire.

Using sulphuric acid and calcium carbonate, you don't get much of a fizz because the calcium sulphate salt formed, is not very soluble, and coats the remaining calcium carbonate inhibiting the reaction. This will happen with any reaction between an acid and a water insoluble reactant which forms an insoluble solid product.

On adding a hydrogen carbonate to an acid, effervescence from carbon dioxide gas is released along with the formation of water and salt. $CO _2$ turns lime water milky.
$ NaHCO _3 + HNO _3 \rightarrow NaNO _3 + H _2O + CO _2 $

On adding a carbonate to an acid, effervescence from carbon dioxide gas is released along with the formation of water and salt. $CO _2$ turns lime water milky.
Phosphoric acid + sodium carbonate $\rightarrow$ sodium phosphate + water + carbon dioxide
$ 2H _3PO _4 + 3Na _2CO _3 \rightarrow 2Na _3PO _4 + 3H _2O + 3CO _2 $

Crushed egg shell has composition $CaCO _3$ reacts with acid and gives gas $CO _2$ which turns lime water $(Ca(OH) _2)$ milky by producing $CaCO _3$ again. The acid in given options is $HCl$. 

When $HCl$ reacts with sodium hydrogen carbonate, the products obtained are $NaCl,$ $H _2O$ and $CO _2$.
$\displaystyle NaHCO _3 + HCl \rightarrow NaCl + H _2O + CO _2$

When $HCl$ reacts with calcium carbonate, the products obtained are $CaCl _2$, $H _2O$ and $CO _2$.
$\displaystyle CaCO _3 + 2HCl \rightarrow CaCl _2 + H _2O + CO _2$

Acid + Metal carbonate  $\longrightarrow$ Salt + Water + Carbon dioxide

CaCO$ _3$ (calcium carbonate-metal carbonate) + 2HCl $\longrightarrow$ CaCl$ _2$ (calcium chloride-salt) + H$ _2$O + CO$ _2$