(1) Heat and work are energy that "sit" in the system True

Reason : ΔU = q + w

according to 1^st law at thermodynamic change in inertial energy equal to the sum of heat and work.

(2) In a reversible adiabatic there is no heat transfer into or out at the system  True

Reason : For adiabatic process, q = 0 always there is no heat transfer take place

(3) During an isothermal process, the internal energy of an ideal gas depends only on the volume False

Reason : Ideal gases have no forces between its molecules, no energy is required to maintain a certain volume in ideal gases. so there is no change in internal energy of system.

In nut shell internal energy of an ideal gas only depends on Temperature it do not depends on the volume.

(4) Change of enthalpy equal to heat transfer for all process False

Reason : ΔH = q 

only at constant pressure not at constant volume temperature

(5) There is no heat transfer in a constant volume process for a system of an ideal gas  False

Reason :According to law of thermodynamies 

Δ U = q + w

Δ U = q - pdv

ΔU = q

( at constant volume Δ v = 0)

It means at constant volume, change and internal energy equal to heat transfer only on temperature.

Hence, the given statement is False