本日も作詩中
making verses even today
Today, too, while I was writing the lyrics,
ふと メロディがおりてきて
unexpectedly it came a melody
A melody just came down from above
ふとそこに言葉がはまる時があって
unexpectedly there's moments that the words falls here
sometmes I get the words that fit there well
自分が聞いてきた音楽の中で
I heard a music inside of me
Among the music that I have been listening to,
大好きな曲の中で
inside a beautiful tune
<-- good!
すごく印象的なフレーズがあって
there's very impressive (effective) phrases ?
<--good. "impresive"
心が衝撃を受ける時っているない？
when my heart (when) not receive a shock ?
いるない makes no sense. It should be just ない. Aren't there times when your heart gets shocked?
一度好きになった歌ってさ
for once (a moment) I loved to singing
The songs that you once fell in love with
ずっと忘れられないよね～
totally unforgettable eh
<-- good
詩が響く曲を書けるように
in order to write music that echoing/resound in the verses
In order to be able to write songs in which the lyrics shine through
頑張ります
I'll do my best
<-- good
明けましておめでとうございます
Happy New Year
good
今年もよろしくお願い致します
I look forward to continuing progress in this year
No! "Please be nice to us this year, too!" This is hard to translate but we say よろしくお願い致します all the time.
やはりご飯食べる隙なく
and as I thought I had no chance to eat / without even getting a chance
to eat
The second translation is good.
予定詰め込みすぎたら
the work piled up on me
Close but wrong. "I put myself on too tight a scedule."
風邪ひいてしまいました
at the end I catch the cold
Yes. "caught a cold"
元旦から1人で寝込んでます
the new year's day I stay in bed all by myself
Yes. "from the New Year's Day"
ゆっくりし
たらだいぶ復活して
きましたが
If I slowly,restful then I'll considerably restored ?
The revival has been slower
(but "tara" it's "if"? but with the 'restored' at the past tense, don't make sense to me)
It makes sense to me. 
たら doesn't mean "if" here. "Because I rested well, I have started to recover (my strength)."
そして最近見た映画では
and from movies I saw recently
Among the movies I've seen lately
バタフライエフェクト３最後の選択
the last choiced, Butterfly effects 3
just a movie title. don't translate it.
が面白かったです
It's been interesting
Was interesting
Please DO NOT ask to help translate a phrase that starts with が. It's impossible! Any beginning Japanese-learner should know that!! No phrase starts with a particle!! Never! 
Grazie!
もし主人公の能力があれば
If I had the main characters power,
Good. "ability/capability", not "power"
僕ならもっと考えるなぁ・・・
I would think more
OK. "I would think twice." or "I would think harder."
なんかふと今なら新しい歌詞が書けそうなそんな気がし てきた
Now something unexpected if is the case new lyric's songs seems I write such feelings ?????
I went "?????", too, upon reading what you wrote! This person speaks more to himself than to his readers, which makes the translations difficult.
"I'm suddenly starting to feel that I could probably write good lyrics if I tried right at this moment."
今から始めます
I'm start from now
yes
今年もたくさんみんなの前で歌えるように
In order to sing in front a lot of everyone even this year
A lot of everyone? It means "a lot of singing" or "lots of songs".
なんかやはりね
things as I thought, isn't?
"Just as I expected"
今日はたくさん言葉が降りてくるんだよね
Today I'd been sommerse of a lot of words, isn't?!
Sommerse?? 
"Lots of words just fall on me (from above)"
詩がたくさん浮かぶ
it inspire / come in mind a lot of verses
"Verses just pop up (without me trying.)"
そんな日もあるよね・・・・
Such days happens too, isn't...?
there are such days, aren't there?
こんばんは
Good night
No! こんばんは never means "good night". It always means "good evening". Good night = おやすみなさい
深夜からこんばんは
good evening from the late night
ＯＫ
今日はもろもろ打ち合わせをしてました
today I did/had a lot of business meeting
Ｇｏｏｄ．
今は家に凛くんが来ております
now I'm going to Rin kun's house
Big mistake here. Read carefully. "Rin-kun is staying at my house tonight."
今年も頑張って行きましょう
let's go (let's get moving) to do the best also this year
OK
風邪だいぶ復活してきました
I restored considerably/ greatly from the cold
OK. The Japanese sentence is incorrect, though. Needs から after the 風邪.
リリースに向けて作業続けております
I continue to go towards work at the rehearsal
Where does it say "rehearsal"? We are continuing to work hard towards the release (of our CD)
ライブの差し入れで頂いたメロン美味しかった！！
the melon I taked at the Live's refreshments was delicious!!
The melon that I received at the concert tasted yummy!