Multi-core transformers combination
1) Will the second circuit give more amperes?


Yes, but not where you want them. See 2).


  2) Is it okay if I connect in parallel 2 transformers with different voltages (in order to increase amperage)?


No. The different voltages will try to correct each other and high currents will flow and, rather quickly, burn out the transformer.


  3) In a multi-core transformer, are all cores independent? For example, If I use one core to power a device, will this affect the amperage of the other core?


Assuming you mean "multi-winding" rather than "multi-core", the answer is that they are somewhat dependent. 


Obviously the total power into the primary will have to be the sum of the output powers plus losses in the core.
If none of the secondary current ratings are exceeded then they can be considered independent except for some droop in voltage caused by increased load.
Each winding will have a maximum current rating regardless of what the load is on the other windings. e.g., A 100 VA transformer with two 50 VA secondaries can only supply 50 VA on each secondary regardless of what's on the other. (In practice it may be possible to push one to 60 VA or more but unless the datasheet says so it would be unwise to use it that way.