The ground is not necessary and has no significance in reality. If the ground is not present, the lower voltage end of the resistor will float with respect to the AC supply, which is fine for most cases.
The wave form for each half cycle will be offset by the voltage across the diodes, as current will only start to flow then the voltage at the low-voltage side of the transformer exceeds two diode drops. There will be a small gap of zero potential ( V=IR across the resistor ) across the resistor when the AC crosses between positive and negative. At this point, the voltage of the more positive wire of the low-voltage side of the transformer will be increasing from zero to say 1.4V wrt the other wire of that side of the transformer. The voltage dropped across the diodes increases until they start to conduct then remains constant ( to a first approximation ), they don't drop 0.7V if you only apply 0.1V to them. So the half cycle starts at 0V then stays there until 1.4V is applied to the bridge, then tracks the sine-wave less the 1.4V diode drops until it hits zero again, then stays at zero until the next AC crossing.