The flow for inserting multi-cut vias for signal routes using NanoRoute is described in this solution article:
For #2, can you clarify what you mean by "without physically connecting it to anything". Have you run SRoute to connect blocks, standard cells, IOs? addRing and addStripe are used to create the power mesh structure and SRoute is used to make the remaining connections. If you go through the tutorial below it demonstrates the flow:
Lastly, if their is a rule in your DRC deck not defined in the LEF you will need to define that rule in the LEF file. The LEF/DEF Reference Manual can be found in cdnshelp or on Cadence Online Support here:
You might check with your foundry to see if they have a technology LEF available to use.