Keeping the name "suwaidah"

Q: I am finding a good name for my baby girl due soon. I am thinking of Suwaidah. I know there is a Sahabah by the name of Suwaid bin Samit, and from the internet I saw that there is a narrator of hadith named Suwaidah. But I couldn't find the meaning of the name. I was told it could have come from the root word Saada, meaning 'Azim/Karim, from which the word Sayyid comes. Is this correct?

Women driving

Q: If my mother is to travel alone to a shop to purchase some item, is it necessary for me to accompany her? She will be driving. Also, if accompanying her will perhaps interfere with my performing of Salaah punctually, what will the ruling be now?

Riyaadul Jannah

Q: It was narrated from Abu Hurayrah that Muhammad (Sallallahu Alayhi Wasallam) said: "The area between my house and my minbar is one of the gardens (rawdah) of Paradise, and my minbar is on my cistern (hawd).

My question is that that will that part of earth be raised into jannah its a duplicate of that part of earth?

Also I heard its shirk to dua from other poeple I mean like you trust into them. Or making dua though someone. Please shed some light on this topic with the opinion of the hanafi maddhab.