Gh can only make a sound like f if it’s preceded by ou or au¹. There are no words in English that begin with gh and make an f sound.

O only makes a short i sound in a single English word: women. This is a weird word and its pronunciation is not permissible anywhere else.

Ti can only make a sound like sh if it is in the middle of a word and followed by a vowel. There are no English words either beginning or ending with ti making the sh sound.

English used to have a voiceless velar fricative sound, represented by the letter h in Old English dictionaries. This is a sound made towards the back of the mouth, like a k that doesn’t fully stop the air. The name Bach ends with this sound, as does the Scottish word loch. English gradually lost this sound. In some cases it was eliminated entirely. In others, it was fronted into an f sound, another kind of fricative. Pretty much all of the weird pronunciations of gh are places where the voiceless velar fricative was replaced. The voiceless velar fricative was allowed as a word-initial phoneme, so you’d think gh with an f sound would be allowed at the start of a word. But it only turned into an f sound if it was preceded by a back, unrounded vowel (a vowel sound in which your lips are neutral and your tongue remains at the bottom of your mouth).Why? Try this: Make an f sound and hold it. Then, open your mouth wide while continuing to exhale and keeping everything else in an otherwise neutral position. Continue trying to make a fricative sound as you do so. You should be able to feel the fricative shift from your lips to the back of your mouth. You’ve just turned an f into the voiceless velar fricative (or something close), and all you had to do was open your mouth. That’s how these sounds are related. But you can’t do this trick with a rounded vowel, like the sound in foot, or a front vowel, like the sound in feet.
The Old English word-initial voiceless velar fricative was either dropped altogether (hlæder → ladder), or turned into an h sound (hēah → high).

In regards to women, the question is not why it’s pronounced as wimmen. The etymology is from wīf which meant woman. (Pronounced weef.) It’s also where the word wife comes from. The ee sound morphing into the short i sound isn’t surprising. The question is why it’s spelled with an o. Nobody’s quite sure how the i sound became an o in the singular. Best guess is that the rounding of the w influenced pronunciation, but people kept the singular and plural pronunciations separate out of utility, and in similarity to pairs like foot and feet. Spelling was then standardized based on the singular with its newer pronunciation, rather than the plural with the older pronunciation.
Why not differentiate the singular and plural by pronouncing the man and men parts differently, as we do in those individual words? English very frequently reduces the vowel sound in unstressed syllables to the schwa, and apparently that rule supersedes. Changing the vowel sound in the stressed syllable must be easier than changing which syllable is stressed.

The ti → sh shift is a result of palatalization. Try this: say ah-tee-on. Now say ah-tchyon. The second should be easier to say. The io diphthong has a palatal y sound in it, which attracts nearby consonants into a single sound simply because it’s easier. Tio and sio easily turn into a sh or ch sound. We have many such words because there’s so much Latin in our language. Latin was able to turn verbs into nouns with the suffix tio or sometimes sio.