Recall that, for node voltage analysis, a floating voltage source (a voltage source that does not connect to the GND node) poses a problem since you cannot write an equation relating the current through to the voltage across.
What you must do then is enclose the floating voltage source in a supernode, which reduces the number of KCL equations by one, and add the equation relating the voltage difference between the nodes the voltage source is connected to.
Now, the dual of node voltage analysis is mesh current analysis and here we have the dual problem when we have a current source common to two meshes - we can't write an equation relating the current through to the voltage across a current source.
What must be done then is to form a supermesh which reduces the number of KVL equations by one and add the equation relating the difference of the mesh currents to the common current source.
So, write KVL counter-clockwise around the supermesh consisting of the two voltage sources and the two resistors
$$V_1 = I_aR_1 + V_2 + (I_b - I_c)R_2$$
You have, by inspection (no KVL required for this mesh - this is dual to no KCL required for the node connected to a non-floating voltage source)
$$I_c = -1.25A $$
You need one more equation which is the equation relating to difference of the two mesh currents with the common current source.
$$3A = I_a - I_b $$
Now, you have 3 independent equations and 3 unknowns.
When analyzing a circuit, you can put the arrows in either direction according to whim, a flipped coin, or Tarot cards.
After applying Kirchoff's laws to compute all the voltages and currents, you'll find some variables have negative values. Those correspond to arrows you drew backwards. Fix those, and then you know the directions of currents in all branches of the circuit.
It is perfectly normal for an experienced engineer to get a few initially backwards, when multiple different voltage sources are pushing in opposite directions. You can only guess, and let algebra tell you the net result.
Best Answer
Yes you treat each node with the "three" bars as connected. Those are ground symbols and are treated as the 0v reference when making voltage measurements. It is also more convenient to show the end of each branch off of the battery with a ground symbol instead of drawing a line all the way back to the battery's negative terminal.
The ground symbol gets its name because it can be used to represent a connection that actually connects to the earth via some conductor buried into the ground. Literal earth connected grounds are usually labeled as such.
*Addition:
You are aware of Kirchhoff's Laws, so we will use the KVL to gain some insight. Imagine a loop going up R3,R2 and back down R4,R5. We know the sum total voltage must be zero. Following that loop we have -30 + VR2 + 35 + 40 = 0. From this we have VR2 = 45V. From this notice that VR2+VR3 = VR4 + VR5, That makes sense they are in parallel. As for the voltage at N1 remember it is referenced to ground. So trace a path to ground and see what the voltage drop is. Starting from N1 down R4 we drop 35V, continuing down R5 we drop another 40V for a total of 75V. So N1 = 75V, Notice this works if you go down R2 and R3.