Best approach to apply for GC for parents of US Citizen

[sbudhraja]

I am a US citizen and want to apply for GC for my mom.

Is there any perceived issue with filling concurrently for I-130/I-485 while she is visiting me on tourist visa?

Is it better to apply via consular processing from the point of view of time for approval and chances of gettting an approval?

Does concurrent filling for AOS and consular processing take the same time or is there a difference?

If AOS is filed concurrently, can she stay in US legally beyond the date stamped at port of entry of AOS is pending?

thanks!