Elite specs ascended weapon collections

My first ever character was a mesmer and once the mirage spec was unlocked I got the Mirage Axe. On this item I had the option to choose between Rabid, DIre and Carrion stats, none of which seemed very appealing to me so the weapon got salvaged. Bad idea, I know. At this point I wasn't aware that the item is part of a collection which can eventually grant ascended weapon.

I have three questions:

1) Can I complete the elite spec collection without the Mirage Axe in my inventory? Must I be in possession of it to get the ascended version?2)How cost and time consuming it is to finish most elite spec collections compared to crafting? Gold is an issue so what will be the cheapest option?3)I already have 2 versions of Caladbolg on my alts. Same question here. Is it cheaper to craft Caladbolg weapons after Knight of the Thorn is completed compared to regular crafting and collection hunting?

1) You do not need it in your inventory. Once it ticks off the collection bit, its job is done2) It's generally cheaper, but there is usually 1 bit in the hot/pof that is expensive, like the mystic coins (hot) or the named exotic (pof)3) I could be wrong here, but crafting a caladbolg outright is very expensive given it needs maguuma lilies which are horrendously over priced vs other mats for ascended. I don't recall it ever being worth crafting it once you got the original from the quest