Trying to understand the names of Allah - like al-Wasi' and al-Hayy

Assalamu alaikum - I was talking with a Muslim friend about a verse that mentions being “in Allah’s mercy.” “As for the bright-faced, they will be in Allah's mercy, where they will remain forever.” (3:108) I had a few questions and our exchange went something like this: Q: Does “to be in Allah’s mercy” mean the same as “to be in Allah”? A: No, it’s different. Mercy is one of Allah’s attributes - ar-Rahman/ar-Rahim - and that attribute existed from the beginning. But some attributes played different roles in creation. For example, the attribute of will was involved even if mercy wasn’t the operative force in every aspect of the original creation. Mercy was especially active in creating humans, sending the Qur’an, and bestowing eloquence (see Qur’an 55:1–4). Q: But isn’t Allah’s mercy described as encompassing everything? (Qur’an 7:156) A: Yes, the attribute of mercy is vast and encompasses a lot. Other attributes, like eternal life (al-Hayy), aren’t described in the same way of “encompassing” creation. Q: Isn’t there an attribute that means “all-encompassing”? A: Allah can be described as encompassing in relation to certain attributes, like mercy (al-Wasi‘). But His essence isn’t something we can contain or fully conceptualize. Q: So “Allah the All-Encompassing” applies to specific attributes only? A: Yes, for example al-Wasi‘ can be applied to mercy or knowledge in the sense that those attributes reach everywhere. Q: So al-Wasi‘ would encompass those who receive mercy, while Allah’s essence doesn’t get divided that way? A: It’s tricky to explain - we shouldn’t think of Allah as divisible. The names describe aspects of His attributes without implying parts or division in His essence. I read a bit about the names and it seems I was mixing up al-Wasi‘ and al-Hayy. Would it be inappropriate to combine names like “Allah al-Wasi‘ al-Hayy” in casual discussion? Any thoughts or clarifications from brothers and sisters who have studied the names and attributes of Allah would be appreciated.