Question about a CMOS operational amplifier
Remember this is a CMOS op amp you are dealing with, so internally it would look like this, you could relate that trans-conductance to that transistor that is right at the output so any output impedance would become parallel to it. This is a model issue so it does not have to be gm per se, but it is a reasonable way to do it generally.


The time is 0+ so for that condition you would consider the capacitor(if it is not charged) to be smaller impedance than the resistance(akin to a close circuit) so most of the current would go towards the capacitor at that instant. Your assumption is correct, but the component that goes to ro would be very small.
Time is infinite so just consider the circuit stable and do each loop following KVL, for Vo ignore the current Co, for Vi it is a bit trickier just think of it like this you got Vi applied to C1 and that goes to ground. C follows what you told us in question 2 and finally do a voltage divider to figure out the relation between Vo and Vi. You need 5.6 to get 5.5 so the order is kinda messed up I would say.










simulate this circuit &ndash; Schematic created using CircuitLab




OTA is a special type of op-amp, it uses diodes on the differential inputs to generate a large resistance on the input. Here is the datasheet for one so you get to know it better. ----> Datasheet