I have virtually no knowledge about L status - are you issued an additional document other than a visa and I-94 (for examples, F-1 students are issued an I-20 and J-1 scholars are issued a DS-2019). Do you have anything similar with an expiration date? If not, then it's the I-94 date that counts, not the visa date.
1- EAD duration is usually based on amount of legal time in the US, not the visa. Once you are inside the US, the visa expiration date is irrelevant - your stay is determined by your I-94 or whatever other document is issued along with your status. But not your visa. So the EAD should remain valid beyond the visa date.
2- EAD is usually valid for 1 year but sometimes less or more in certain situations. If your I-94 expires in less than a year, then the EAD may be valid only until the I-94 expiration date.
3- USCIS can ask for anything it wants, but unlikely it will ask that.
4- Usually EADs are issued in fewer than 3 months (4-8 weeks sometimes). My wife once got hers in 10 days.
5- She will be working illegally if her EAD expires and her new one doesn't arrive. The 180 day thing is not permission to work, it is a stipulation that USCIS may forgive somebody for working illegally if such work was less than 180 days - but that is subject to certain conditions. It is in no way "legal" to work for those 180 days.