@YanagiPablo With all due respect, I agree with Zizka on this one. Numbers or letters might be easier for newcomers to follow. The other thing is that the most common system for ordering the kana, to my knowledge, is the Gojūon system. I’ve seen it used in Japanese bookshops and on kana keyboards. However, I can see from the Wikipedia page that the Iroha system, while not necessarily older, is more traditional, and has even found its way into some expressions, so I really appreciate your choice. I learnt something today.
To start the ball rolling, I’ll try handling イ (while following the rules this time):
イ/A
Literal Translation
すっかり よく なりました ね
completely good-adverbial become-polite-past [agreement]
午後 には 退院 できる ように 手続き を とって おきましょう
afternoon [time][emphasis] back-away-hospital able-to-do manner-in procedure [object] take-TE put-polite-volitional
Interpretation
You've become completely/much better, huh?
すっかり means ‘completely’ or ‘thoroughly’ and (perhaps by extension) ‘very’. My way of remembering it is to think of すべて(全て), but there are other similar words starting with す that have slightly different meanings, so it’s up to you if you want to adopt my mnemonic.
よく is the adverbial or ‘declinable-connective’ (I’m making this term up. The Japanese technical term is 連用形, which are the forms that link to 用言, declinable words.) form of いい/良い. This form of adjectives is used with なる to mean ‘to become [adjective]’.
ね as always indicates that agreement is being sought or is expected by the speaker.
Let's do the procedures so you'll be able to be discharged from the hospital this afternoon first.
午=midday; 後=behind/after
退院=the act of leaving the hospital
Use of できる: 〜する verb (to do ~) → 〜できる verb (to be able to do ~)
ように: よう indicates a certain state or condition. に indicates an aim here, in my opinion. Thus, ‘in order to be able to leave the hospital this afternoon…’
手続き: procedures. 続き is the noun/continuative form of the verb 続く, which means ‘to continue (intransitive)’. I don’t know how to explain the logic behind it because this expression exists in Chinese too (手续)… it literally means ‘continuation of/for the hands’. Just imagine handovers. They require a lot of work with the hands [手] (filling out administrative documents and so on) in order to ensure continuity [続き]. The construction for ‘to do the procedures’ is 「手続きを取る」, hence what’s written in the dialogue.
ておきましょう: the -ou ending is characteristic of the ‘volitional’ form, which indicates the speaker’s will or desire to do something. Here, the speaker is proposing that the discharge procedures be done ‘first’ or ‘beforehand’. This is indicated by the use of おきましょう, which comes from 置く, meaning ‘to put’. When used with the て-form of a verb, it means the action that that verb indicates is done first or before others. You can think of it as doing something first and putting it aside. As a side note, 置くis also used in mathematical proofs to mean ‘let’ (“soit” in French), as in
「I=[1,2] と置く」
meaning ‘let I be the interval [1,2]’.
PS: I find a separate ‘vocabulary’ section a little tiresome. To me, it’s basically what each of us would find in a dictionary. I think explaining all the above took me 1-2h. Is it alright if I continue with this ‘literal translation’/‘interpretation’ format, possibly with less detail? I can use fewer technical terms as well, if you prefer.