Not automatically, but you can configure it to mirror certain video channels or individual videos. But I have not looked into that too much yet.
As for storage: a typical video you would find on such a platform with the different stored video resolutions and so on will take between 0.5 and 3 GB... depending on the length and how well it compresses.
@Sunny@slrpnk.net already has an XMPP account, as that is included in every slrpnk.net account automatically. It is very easy to set that up for most Fediverse software, and the user id is identical between Fediverse and XMPP.