1) Negative/positive feedback with only passive components, whether this makes sense at all?
Listing the book about signal processing i found 
Negative feedback with only passive components
operational-amplifieroscillator
Related Solutions
See my answer here for an example of why you might want to use negative and positive feedback at the same time. The 598.3K resistor in the positive feedback path maintains a constant current through the variable resistor and the negative feedback path determines the gain (output volts per ohm of resistance of the variable resistor).
To see how this yields a constant current, consider Scott's generalized NIC answer. This is also a NIC- creating a negative resistance to cancel out the incremental effect of the 100K resistor R2, so the current remains constant.
Looking into the non-inverting input of the op-amp (without R2 and the variable resistor connected, but with R4 in place), the resistance looks like:
Referring to the NIC schematic, we have:-
R1 = 100K || 25.68K = 20.43K R2 = 122.2K R3 = 598.3K
\$ R_{IN} = \$ - 598.3K \$ \cdot \$ \$ 20.43K \over 122.2K\$ = -100K, which exactly cancels out the effect of the 100K resistor R2 (R2 on the original schematic).
"So why do we only assume negative feedback takes place"
It is not correct that "we assume negative feedback" only. Who say this?
The shown two-opamp circuit (introduced by A. Antoniou) can be interpreted as a combination of two "Negative Impedance Converter (NIC)" circuits. There are two basic NIC types (current-inversion - INIC, and voltage-inversion - VNIC) and both exhibit a negative input impedance. However, a stable combination results if we replace the grounded output resistor of the first NIC unit (INIC) with the negative input impedance of the second NIC unit (VNIC).
This forms already a circuit called "Generalized Impedance Converter GIC". However, this form has some disadvantages - and therefore a modification is used which is known as Antonious GIC circuit (as shown in the question). It is easy to show that this alternative has the best properties of all possible modifications - as far as influence of real opamp parameters is concerned. This form can be derived from the simple NIC combination exchanging some opamp input nodes which are (for ideal opamps) at the same potential.
This GIC is extensively used in active filter realizations as an "active inductor" and/or as a "Frequency-Dependent Negative Resistor (FDNR)".
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Best Answer
I'm not sure that you gain much understanding by looking at this as a feedback circuit, but the equations certainly work. I suppose it make it real easy to see that as V goes to the point where i2=i, then i1 goes to zero.