How to analyze a capacitor in series to a capacitor and resistor in parallel?
You have a major misunderstanding. You wanted to apply formulas which are valid for a circuit which has one resistor and one capacitor. To solve the behaviour of more complex circuits you must learn to derive equations for it starting from the circuit and general circuit laws. Systematic methods for it - general ones and methods for limited cases such as single frequency sinusoidal voltages and currents - have been well known well over 100 years. Then you must be able to solve the equations to get the formulas which are valid for your circuit (=a common feedback circuit in low frequency oscillators, the Wien Bridge). Circuit analysis books present those known methods and have plenty of practicing material.

If it happens that you are trying to analyze this to get the frequency of a Wien Bridge oscillator you should learn how to apply phasor calculus with complex numbers or Laplace domain transfer functions. Or search the result from handbooks or web. Sorry!