How tension force is shown going through a body in this problem even though tension is a pulling force? I was solving some problems about tension forces in my textbook and in solution of one problem I saw that one of the tension forces is drawn through the body,which confused me because text book was always drawing tension forces out of body(because it always pulls the body).
The Problem

Textbook Solution

The solutions follows like this:
I.$$T_{2}<T_{3}$$ because its just a component of T3 obviously.
II.$$T_{1}=T_{5}$$ because purple tension forces cancel each other out.
III.$$T_{2}=T_{4}$$ because they are only horizontal and they cancel each other(green ones).
My Question
I am actually confused at more than one point.These are point that I am confused at:
I. How did we know that T2 and T1 is component of T3 and do the two opposite T3 forces cancel each other out?
II. I dont get how we can say that there is T5 thats going through the body even though tension is a pulling force.
III. I am ok with this step because it is obvious.
I will appreciate any help and would be really happy if you can end my confusion.
 A: A very intuitive way of looking at this problem is by removing the T3 rope and connecting the joint points of  T4, T5 with T1, T3. By doing so, you can obviously see that horizontal and vertical components are equal.
And about T3, you could assume an angle and use cosine law to see that T3 is actually bigger than each of T1 and T2, but you could also argue since vertical component of T3 is equal to T1 and horizontal component of T3 is equal to T2, then T3 must be greater than T1 and greater than T2.
A: Tension force arises from the tendency of elastic ropes to maintain their length. Hence, it acts both ways. Imagine a game of tug of war between you and your friend. You feel a force in the direction opposite to the direction you are trying to pull the rope, and so does your friend. This is a good way for getting an intuition for how tension forces work. They work only when the rope is taut and act on both ends, being opposite to each other in direction.
The system given in the problem is in equilibrium as none of the points has any acceleration. Therefore, forces must be balanced at each point.
Now, let me tackle your confusions:

*

*$T_2$ and $T_1$ are not components of $T_3$, they are equal to the horizontal and vertical components of $T_3$ respectively. I have already mentioned the reason why.

*I do not understand your confusion here. Perhaps you need to strengthen your understanding of the nature of tension forces.

