Dear ayelamayem!
I don't have either ETABS2013 or SAFE2014, so my comments are based on general concepts of CSI software, and with reference to earlier versions of ETABS & SAFE.
Comments on your specific questions, are as under:
1. IMO, yes. The load effects due to lateral loads would NOT be transferred properly and completely, using this option.
2. Yes. You may provide stiff or thicker slab areas under the columns. This is required in most of the cases (due to heavy column loads, and to satisfy shear requirements), and is possible to provide, even in older versions of SAFE.
3. This is a complex issue, and relates to newer versions of CSI software. As such, you will probably need to contact CSI directly for clarification in this regard.
HTH
Regards.