发 is one simplified glyph standing in for two different traditional characters. This is the first thing to fix in your mind, because it is the key to everything else on the page. Where the mainland writes a single 发, traditional script keeps two separate forms with two separate readings:

發 fā, the older and busier word, meaning to shoot, send out, emit, issue, or develop. The traditional 發 is built around 弓 (gōng, bow) and a foot element, the picture of loosing an arrow: to send something flying from oneself.
髮 fà, meaning the hair of the head. The traditional 髮 carries 髟 (biāo), the long-hair radical that sits atop characters about hair and beards.

When the script was simplified both 發 and 髮 collapsed into the same cursive-derived shape, 发, classified under the radical 又 (yòu, a hand). The merge saves strokes but loads one glyph with two unrelated meanings and two tones. So 发 is a true polyphone: read fā (first tone) for the send / emit / develop family, and fà (fourth tone) for hair.

The fā senses fan out from the core image of loosing something outward. To send: 发送 fāsòng (to transmit), 发出 fāchū (to give off). To bring forth or grow: 发展 fāzhǎn (to develop), 发现 fāxiàn (to discover), 发明 fāmíng (to invent). To occur, as if an event were loosed into being: 发生 fāshēng (to happen). To issue formally: 发表 fābiǎo (to publish). The fà sense stays put on a single concrete thing: the hair, 头发 tóufa.

The same outward motion that sends an arrow flying also drives the sense of growth. When something 发 develops, it is unfolding from a small start into a fuller state, the way a bud loosens into a flower. 发展 fāzhǎn (to develop) is one of the most common verbs in modern Chinese, anchoring talk of economies, careers, technology, and people. Beside it sit 发现 fāxiàn (to discover, to bring a hidden thing into view), 发明 fāmíng (to invent, to bring a new thing into being), and 发育 fāyù (to mature physically).

A third branch of fā treats an event itself as something loosed into the world. 发生 fāshēng means "to happen, to occur," literally to send-forth-life: an accident, a war, a change all 发生. The English "break out" catches the flavor, an event bursting into being rather than quietly arriving.

Here is where the merge bites. The single character 发 also reads fà (fourth tone) and means the hair on a head, a meaning written 髮 in traditional script and entirely unrelated to sending or developing. The reading you choose is fixed by the word:

Say fà in the hair words: 头发 tóufa (hair, though the suffix here is toneless in everyday speech), 理发 lǐfà (to get a haircut), 白发 báifà (white hair), 长发 chángfà (long hair), 短发 duǎnfà (short hair).
Say fā everywhere else: 发送, 发展, 发现, 发生, and the rest of the send / develop family.

A clean test: if the word is about what grows on your head, it is fà; if it is about something leaving, growing, or happening, it is fā. The two never overlap in meaning, only in the simplified glyph that now carries both.

Hold two pictures side by side, because 发 is two characters wearing one face. First picture: an archer looses an arrow, fā. That single act of sending outward is every fā word, the message sent (发送), the sound given off (发出), the bud opening into growth (发展), the discovery brought to light (发现), the event bursting into being (发生).

Second picture: a single strand of hair, fà. That is the other 发 entirely, the one traditional script wrote as 髮, surviving in 头发, 理发, 白发. The tone is your switch: rising-from-rest first tone fā for sending and growing, falling fourth tone fà for the hair on a head. One glyph, two stories, kept apart by a single tone.