They're entirely different letters. They generally sound the same, though some speakers still articulate them distinctly.

Kaf/khaf (כ) makes the same sound as het (ח) in Modern Hebrew when it's soft, but the distinction is that in hard positions כ, also written כּ‬ in these instances, with a dot in the centre space, makes a /k/ sound. Traditionally soft khaf is pronounced further back in the thoat, but that distinction has been lost in common speech.

Not much... at the end of a word they do diffrent things. The כ sounds like CH/CHA and the ח sounds like ACH (EG. תפוח = apple = Ta-pu-ach) (EG. לך = (for) you = le-cha) (EG. איך = how = e-ch)

not the best exemples but that what I could think right now... Anyway at a middle of a word it is only memory

Its pronounced different. "ח" is more like "h", and "כ" is more like "k". Beside that I dont see any patterns.

Because in these cases, like in "אוהב", it is only meant to stand as a proxy for a vowel, here "o". So if you had punctuation/niqqud, there would be a small dot on top of the "ו", and that would be all you're supposed to actually read.

It can be v, o, or u. ;)

in short, it's because it also doubles as two separate vowels. in more detail it's because in Hebrew vowels are in the form of stuff called 'נקודות' and the letter 'ו' can only really be a letter, but it's just that there are two 'נקודות' that look similar to 'ו' but have a dot in one of two positions. the thing is that on a keyboard, you can't write 'נקודות' without the hassle of a lot of copying and pasting and even on a pencil and paper, people typically don't write 'נקודות' unless not specifying which one leaves various options that can mean different things