Number of cycles for AGM battery with an inverter
There are really two questions here.


To calculate the run time you first need to estimate the amount of
current being drawn by the inverter. If you assume an efficiency of
85% (your millage may vary) then you can calculate the current as
((120V / 24V) * 7A) / 0.85= 41A.  This number is a bit on the high
side since the voltage will initially start around 26V and drop down
as you discharge the battery. The run time for 50% discharge is then
calculate as  a)  (200 AH/41A) / 50% = 9.7 hrs.  In case b) you have
double the capacity so the runtime is increased by two.
You don't get any more charge discharge cycles by combing batteries in series. However, if you combine them in parallel then you would only be discharging the banks by half as much for a given a given amount of time. So even though your charge/discharge cycles wouldn't change, you would get twice as much work out of the batteries.