Operational Amplifiers problem
To answer your first question about the node between R4 and R3 you have to decide if the feedback is positive or negative. I'll leave that up to you but if you conclude that the feedback is positive then the answer is a certain "no" and both op-amp outputs will be pushed against the power rails in saturation.

If you decide the answer is "yes" then, as a first approximation, the voltage at the node of R4 and R3 will be equal to Vin. If you took a more detailed look into op-amp behaviour the answer would almost certainly be "not quite" or "no". This is because there are offset voltages to consider and leakage currents from the inputs to consider - these make the perfect op-amp "imperfect" and you'll find that there will be a small error voltage that can rage from a microvolt to several millivolts. Non-infinite open loop gain also erodes the chances of both inputs being equal.

If you then looked deeper into the workings of the op-amp, you should conclude (op-amp dependant) that at relatively high frequencies, the feedback becomes positive and in fact the configuration you have will likely "sing" at some obscure frequency in the high tens of kHz to several MHz.

But, assuming perfect op-amps, you assume the two input voltages are equal and work backwards from that presumption....

The output from A2 will be 

\$V_{IN}\times \dfrac{R_3+R_4}{R_4}\$

And, the output from A1 will be smaller than the output of A2 by the factor R2/R1

From this you should be able to solve your question.