1: No hard-and-fast rule, it depends on the magus. Only Faerie Calling is expressly trumped by Twilight.
2: Have the Gift, and swear the Oath in the presence of a magus willing to sponsor you. Boom, magus.
My understanding of House Ex Misc is that pretty much anyone can join, and the Gift is not even a requirement. Un-Gifted hedge magicians are welcome and, according to history, have been members before. For example, when the House was founded by Pralix, most of the new House was made up of unGifted hedge magicians from the British Isles who were veterans of the Spider War: beast masters, malice writers, weather witches, and so on. The Gifted members of these traditions rose to leadership roles, but they had more unGifted followers.
The House today is so disorganized that there is a history of wizards hiding inside the Order by claiming to be members of Ex Misc and simply getting away with it, even though they never actually joined that House, or may even belong to a different House or be a Hermetic outlaw. You can get away with this if you don't attract attention, because the records of Ex Misc are so disorganized that even the House leadership doesn't have a complete count.
Your campaign also may link this to the mystery of the leader of Ex Misc, who is known to have come from a different House, but which House is never clarified. If it is, as many suspect, House Tremere, he may be trying to bring a new level of organization and structure to Ex Misc, for Tremere's usually dubious motives, of course. (House Tremere: 400' years of doing the right thing for the wrong reasons!)
HMRE pg. 6. The Gift is a requirement for membership in the Order, Redcaps excepted. There are some groups of hedge-wizards with both Gifted and unGifted members, where the Gifted ones joined the Order while the unGifted ones either serve the Gifted ones or are mostly ignored by the Order (see: the sorginak).
This text only says, that the Gift in general is a requirement, but that no Code rulings explicitly require magi to have it. Then it outlines in two paragraphs, which exceptions beyond Redcaps might be possible.
IIRC it's based on the first tradition to which the Gift is opened. I may be wrong. If there is an official stance on this, it should be in either Hedge Magic Revised Edition or in Rival Magic.
Swearing the Oath. Full stop, end of story.
In the 4th edition, the Hedge Magic book suggested some ability/-ies might be needed. Mainly Latin 3.
Formally speaking, I suppose a House would also need to accept you as one of their own, but given how loose House Ex Miscellanea tends to be, that shouldn't be much of a problem.
Hermetic and non-Hermetic magic interactions probably depend very much on the combination of traditions.
Nominally, joining the Order and House Ex Miscellanea requires a sponsor and swearing the Oath. Without a sponsor, you are simply a magician who has claimed to swear the Oath (although the test would be simple - repeat it). A sponsor stands in for your Hermetic master, and presumably affirms that you have some kind of magical power (although what, how powerful, and whether other magi would agree is an open question). Your Oath still needs to be witnessed by a third party, probably a quaesitor.