Jitensha (自転車)

Yesterday, a-little hair (object) cut

髪を切る ('to cut hair') is what you do at a 美容院 (beauty salon) for women or 床屋 (barber) for men. The verb 切る also means cut in the abstract sense — 関係を切る ('cut ties').

Don't-say if, surely, anyone (intensifier) wouldn't-notice probably but

Verb-negative-ば conditional: 言う → 言わない → 言わなければ ('if I don't say'). Standard 'if not X' construction. Pairing with だろう adds the speculative 'probably' tone.

Several-months's worth's I (subject) floor onto fell (nominalized) (object) saw

Noun + 分 ('worth of / amount of'): 何ヶ月か分 ('a few months' worth'), 二日分 ('two days' worth'), 一週間分 ('a week's worth'). Useful for measured amounts. 落っこちる is the casual/childish version of 落ちる ('fall').

Eyes (object) closing, started-being-audible rain's sound

Verb-て + くる ('come to') marks something approaching the speaker's perception or location. 聞こえてくる ('to come into hearing / become audible'), 見えてくる ('to come into view'). The sound of rain 'comes to' the listener with eyes closed.

Title chant — bicycle ×3

自転車 (じてんしゃ) literally 'self-turn-vehicle' — the standard word for bicycle, common in everyday Japanese life. The title's repetition becomes a chant — like the rhythm of pedaling.

Right-now, meet-to, let's-go

Verb stem + に + 行く ('go to do X') is the standard purpose-of-motion construction: 食べに行く ('go to eat'), 買いに行く ('go to buy'), 会いに行く ('go to meet').