1. Write the equilibrium and count gaseous moles

Given: $\mathrm{CO}(g)+3\mathrm{H}_2(g) \rightleftharpoons \mathrm{CH}_4(g)+\mathrm{H}_2\mathrm{O}(g)$

Number of moles of gaseous reactants: $1+3=4$

Number of moles of gaseous products: $1+1=2$

So, the reaction goes from 4 moles of gas to 2 moles of gas.

2. Effect of increasing pressure at constant temperature

If pressure is increased twofold at constant temperature, the equilibrium shifts in the direction with fewer moles of gas according to Le Chatelier’s principle.

Since products side has fewer moles of gas, equilibrium shifts forward.

So, statement (B) is correct.

3. Check statement (A)

When pressure is increased by decreasing volume at constant temperature, the concentration of all gaseous species increases immediately because: $C = \frac{n}{V}$

If volume decreases, concentration increases.

Thus, concentrations of both reactants and products increase initially.

So, statement (A) is correct.

4. Check statement (C)

Equilibrium constant depends only on temperature.

Since temperature is constant, equilibrium constant does not change, even though equilibrium position may shift.

Therefore, statement (C) is false.

5. Check statement (D)

Statement (D) says equilibrium constant remains unchanged as concentration of reactants and products remain same.

This is incorrect because although equilibrium constant indeed remains unchanged at constant temperature, the reason given is wrong: concentrations do not remain same when pressure is increased.

Hence, statement (D) is false.

6. Select the correct option

Correct statements are: $\boxed{(A) \text{ and } (B) \text{ only}}$

Therefore, the correct option is: $\boxed{\text{A}}$