Having no SWR is a good thing and shows your radio is working well.
SWR stands for "Standing Wave Ratio". In a perfect world (and a perfect antenna) all power will be radiated. An antenna is a system and is compiled of may things. When you get you hand close. or on, the antenna you are part of the system. You then 'de-tune' the system, creating a less than perfect radio radiator and it creates standing waves.
The standing waves are basically wasted power. And if that power (SWR) gets really high is can damage the transmitter. Fortunately we are working with very low power so I shouldn't damage the transmitter.
The RSSI jumping could be because you are indoors and the signal is bouncing off the walls and causing multipath errors.