Traditionally, Rogues have been/are both nimble and perceptive (think Spot and similar checks, in previous editions; and in 5E, that Rogues can be proficient in Insight, Investigation and Perception). The fact that you start with at least 13 Wis attests to your even higher acuity (relative to other rogues). So, a few things:

• Unarmored Defense can be attributed to improving your dodging (through practice) and ability to read and anticipate your enemy's movement. At least, that's how I interpret the Monk's ability to add Wisdom (which is tied to Perception and Insight) to their AC: the higher AC is based on perceiving and having better insight into the enemy's body language, what that reveals about their next attack, and how the Monk can then make sure to not be where the enemy is about to strike. You soon realise that your armour is only getting in the way by slowing you down: your eyes provide you with enough information to dodge with greater success than the protection offered by your armour, which is only preventing you from dodging fast enough.
• Unarmed Strike is a bit trickier, BUT, if you're willing to compromise, you actually don't have to compromise ;): just use a shortsword (a Monk weapon that also has finesse) from the get-go, and there's no weapon transition. Re: the extra unarmed strike, you can also chalk it up to grinding/self-improvement (like above): your above-average dexterity has enabled you to strike so swiftly with your short sword, that you can also deliver a decent punch (one that will continue improving the more you train).
• Ki might be the harder one to explain, but here goes: As you continue fighting and gaining insight into your own body and abilities, you begin to discover ("stumble with") a source of energy that you had never felt before (think Neo, in the Matrix, when he first is able to deliver super-fast punches): you don't really know how it happened, you just know that you 'tuned in' to something inside you, and went beyond what a mere mortal could do. You also realise that this energy is limited, but as you continue training, you feel the pool growing inside... together with a wider range of super-human abilities that it can fuel.

(I'm omitting Shadow Monk discussion because we already covered that at length, in our chat)

Traditionally, Rogues have been (are) both nimble and perceptive (they had Spot and similar skills as class skills in previous editions; and in 5E, Rogues can be proficient in Insight, Investigation and Perception). The fact that you start with at least 13 Wis attests to your even higher acuity (relative to other rogues). With that in mind, a few thoughts:

• Unarmored Defense can be attributed to improving your dodging (through practice) and ability to read and anticipate your enemy's movement. At least, that's how I interpret the Monk's ability to add Wisdom (which is tied to Perception and Insight) to their AC: the higher AC is based on perceiving and having better insight into the enemy's body language, what that reveals about their next attack, and how the Monk can then make sure to not be where the enemy is about to strike. You soon realise that your eyes provide you with enough information to dodge with greater success than the protection offered by your armour; you're so good, in fact, that your armour is only getting in the way by slowing you down.
• Unarmed Strike is a bit trickier, BUT, if you're willing to compromise, you actually don't have to compromise ;): just use a shortsword (a Monk weapon that also has finesse) from the get-go, and there's no weapon transition. Re: the extra unarmed strike (via bonus action), you can also chalk it up to grinding/self-improvement (as above): your above-average dexterity has enabled you to strike so swiftly with your short sword, that you can also deliver a decent punch. As you continue practicing this new-found technique, you find that you can deliver more and stronger punches.
• Ki might be the harder one to explain, but here goes: As you continue fighting and gaining insight into your own body and abilities, you begin to discover ("stumble upon") a source of energy that you had never felt before (think of Neo, in the Matrix, when he is first able to deliver super-fast punches): you don't really know how it happened, you just know that you 'tuned in' to something inside you, and went beyond what a mere mortal could do. You also realise that this energy is limited, but as you continue training, you feel the pool growing inside, together with a wider range of super-human abilities that it can fuel.

(I'm omitting Shadow Monk discussion because we already covered that at length, in our chat)