The full texts of these abilities are "At the beginning of the monarch's end step, that player draws a card" and "Whenever a creature deals combat damage to the monarch, its controller becomes the monarch." (2020-11-10) If the triggered ability that causes the monarch to draw a card goes on the stack and a different player becomes the monarch before that ability resolves, the first player will still draw the card

Hogback [Wings of the Captain] $1.50 AUD Gum-Gum King Kong Gatling [Wings of the Captain] NM $1.50 AUD Hody Jones [Wings of the Captain] $0.50 AUD NM $1.50 AUD $0.50 AUD Aramaki [Wings of the Captain] $2.00 AUD Lily Carnation [Wings of the Captain] $0.50 AUD $0.50 AUD Absalom [Wings of the Captain] NM $1.50 AUD Vander Decken IX [Wings of the Captain] NM $1.50 AUD Yamato (Alternate Art) [Wings of the Captain] $122.30 AUD Uta (Alternate Art) [Wings of the Captain] $61.20 AUD Negative Hollow [Wings of the Captain] NM NM $1.50 AUD Tot Musica [Wings of the Captain] NM $1.50 AUD Black Bug [Wings of the Captain] NM $1.50 AUD Cosette [Wings of the Captain] NM $0.50 AUD Cerberus [Wings of the Captain] $0.50 AUD $0.50 AUD Nami (Alternate Art) [Wings of the Captain] $507.20 AUD Ms
Since you can always see the top card of your library, Traveling Chocobo lets you plan your turns ahead with the knowledge of what you're drawing if you can't play it
(When this Equipment enters the battlefield, create a 2/2 red Rebel creature token, then attach this to it.) Whenever Blade of Shared Souls becomes attached to a creature, for as long as Blade of Shared Souls remains attached to it, you may have that creature become a copy of another target creature you control