Resonance arises from the fact that when you have an inductor and a capacitor in series, while the capacitor is being charged the current flowing induces a contrary voltage at the inductor, so in series the voltages sums to zero, this let the source to charge the capacitor to higher voltages as it appear like a short circuit for the source. When the current decay the voltage across the inductor becomes smaller while capacitors voltage raises. This is why an inductor has a voltage peak that appear 90° before the capacitor peak voltage.

There are 360° for a complete cycle, so lets examine it:

Consider the capacitor is not charged initially

1° 90° The current is maximum so as voltage across the inductor. The voltage of the inductor is a cosine function, while the capacitors voltage follow a sine function up to its max voltage

2° 90° current stops, and the capacitor completely discharge into the inductor.

3° 90° the inductor charge the capacitor with reversed polarity

4° 90° the capacitor discharge into the inductor.

Summing to that, at the end of the cycle, when current is zero, the capacitor has the full voltage across it, and the polarity is inverted, so you can aways add more energy to it. Because as you apply a contrary voltage to a capacitor charged the, energy at the end will be the sum of the energy you inputed + the energy originally at the capacitor.

Its known that the time constant for a capacitor depends on its capacitance and the resistance in series.

As a Capacitor accumulates a charge Q the peak current will depend on the time constant.

If you discharge the capacitor applying a contrary voltage to it, would the RC time constant be the same?

I think would become smaller, because you are forcing it so the peak current will be greater...

Of course resonance voltage is only limited by the real resistance of the circuit and to the voltage applied...

The resistance will affect the phase limit between voltage peaks therefore it will limit the resonance not only by dissipating power but impeding the voltages in series to completely cancel out.