.... hmm where to start...
1. No if the grid tie is put on the outputs of the inverter it will run backwards through the transformer and synchronously switch the ac to dc and charge the battery... but with no control. Your point #2 tells us that there is filtering on the transformers, so the grid tie will work.
3.... yes and no........ as a general observation, as the batteries come out of bulk charge, their needs become dramatically less, ie where they may have been charging at 60amps, they will drop down to 10 and much less when they are 90% charged.
The effect of this is that the AC being generated by the grid tie inverter will force the AC voltage higher, and there is an excellent chance the grid tie will drop off of it's own accord because of high AC... thats what happens with mine anyway. I built a battery voltage switch to do this, but found it does it on it's own anyway, so I have two systems to shut down the over charging that would have occurred if this did not happen one way or the other.,... neat.
If your battery bank is at least500ah@48v, you will be able to charge at 100 amps max... or 5kw or there abouts, but it will soon drive the AC or the battery voltage up too high, and shut down either the inverter (PJ) from high battery voltage ( 61 or 62 ) which is annoying, or high AC which will drop off the grid tie inverter... which will try again in another three minutes etc etc etc.
So a battery over volt switch is really a very good thing to install.
However, once you bring your real grid into this mess, your better not to do any of that!!... they will take a dim view of this.
Your best to run a battery charger and float the batteries until the outage, and carefully use the inverter then.... you should not switch or change the grid tie arrangements from what you were contracted to do originally, or they may kick you off the feedback tariff, or shut your grid tie down if you piss them off enough.
You should have interlocking isolating switches before you even consider this, as it must be the case that NO power from you can get to the grid from your PJ or any other AC source when the grid is down, or someones death may occur.... very slim, as the impedance of the dead grid will be very very low... but it can happen in the right circumstances..... take note..... this is serious.
However if you have a secondary household circuit not connected to the grid in any way, then you can power that..... or use extension cords and lots of power blocks etc etc...... but don't mess with the grid unless you know what your doing. Normally it is just you who is at risk, but with backfeeding by mistake, it is not just you.
So...
1. don't use your grid tie to inverter to charge the batteries in this case, this is for off grid use... and very useful it is too... but not to be mixed with the real grid.
2. your idle figures are superb...
3. use a charger to float the batteries from the grid. They will be isolated by the transformer ( HF or LF), and will not interfere with your contract with the power supplier, and your grid tie will be driving the grid anyway.... all wins no losses if you use a timer to not charge or not float charge during the night... say only turn charger on between 10am and 4pm etc etc.
4. work out how you are going to use your PJ when the power does go off.
................oztules