So let's say Mairsil, the Pretender exile Vorpal Sword and copy the "a player lose the game" activated ability. Does it work? Mairsil need to have at least any equpment to be an "equipped creature"? Doesnt do anything at all?
Also, let's say Mairsil has the ability of The Deck of Many Things (or any D20 dice roll card for that matter). It's all the card one only activated ability and works normally with Mairsil?
Assuming Vorpal Sword is a card you own in exile with a cage counter on it:
Although Mairsil will gain both activated abilities of Vorpal Sword (even the equip ability) and both of those abilities can be activated, you can't attach Mairsil to anything if it's a creature or if it's neither an Aura nor an Equipment nor a Fortification (C.R. 701.3b, 301.5c, 702.6a). (Notably, "equipped creature" here means the permanent that Mairsil itself is attached to [C.R. 301.5e]).
As for your second question: See comment 4.
EDIT (Jul. 13): Edit in view of release notes.
EDIT (Jul. 23): Edit in view of rule update.
The activated ability, when it resolves, would give to Mairsil the triggered ability "Whenever equipped creature deals combat damage to a player, that player loses the game". In order for this triggered ability to work, Mairsil would need to be an equipment equipped to a creature. Mairsil being a creature with an equipment wouldn't, ahem, cut it.
We don't yet have the full rules that explain how a d20 ability such as The Deck's works. My informed guess is that it's all a single activated ability, so it would work with Mairsil normally.
The rule update for Adventures in the Forgotten Realms is now available.
As clarified by C.R. 706.3b, "[a]n instruction to roll one or more dice, any instructions to modify that roll printed in the same paragraph, any additional instructions based on the result of the roll, and the associated results table are all part of one ability". Thus, for example, The Deck of Many Things has a single ability for purposes of Mairsil.