As I understand voltage of the circuits could be different in absolute term, so that's one of the reason we make the ground.
Ground can be connected to earth or it can be just a convenient point in a circuit to provide a reference when measuring voltages to any other point.
One of my fear about working with circuit, especially when I use multimeter with the circuit power on, is that my multimeter probe makes electric spark with the circuit.
On voltage range the multimeter will have a high input resistance. For most digital meters this will be about 10 MΩ. The current drawn by the meter is so low that it will never spark.
You could cause a spark by bridging out two points on a circuit with the probe. Many now come with removeable insulating tips so that, when in place, the exposed tips are tiny and a short circuit is unlikely.
A common mistake is to forget to switch the probes back to the correct sockets after taking a current measurement. The low resistance of the current shunt provides a near short-circuit. This is dangerous and cheap meters can explode if the user takes a mains voltage reading while the probes are in the current and common sockets.
I am not sure if I am paranoid or using my multimeter in a wrong way.
A little bit of fear is good.
But in my mind my multimeter uses 9V battery and the circuit uses whatever power regardless grounded or not. Then, because these are two different power system, isn't there some possibility of electrical spark on the moment that I approach the circuit with the circuit?
No. The 9 V of the battery is not applied to the inputs.
Probably if I measure between the ground of circuit and the point in the circuit that would be mostly okay as I can think my multimeter and the circuit is common grounded. But what if the points in the middle of the circuit? Should I attach my probes first before powering on the circuit?
It won't make any difference to the meter but it may protect you from injury when working on voltages > 50 V.
My answer to Ambiguity in voltage measurement may be of help.
Figure 1. The building on the ground and shot off into space. In the space situation (electrically isolated) we can call any floor the 'ground' floor. [Image by @Transistor.]
In Figure 1 we have called the ground floor 0 (as is European practice). Floors above are numbered 1, 2, 3, ... and floors below, -1, -2. We can now calculate the number of flights of stairs to climb by subtracting the start from the end. So to travel from -1 to +3 we need to climb 3 - -1 = 3 + 1 = 4 flights.
Note that we could pick any floor as "ground". It doesn't matter - it's just a reference.
