It is certainly not required in English to put a possessive on any noun that could have a possessive. However, it is conventional to use a possessive on objects that are closely associated with a person, like parts of his body or the clothes he's wearing, especially when without a possessive we would have to put an article.
It would not violate any rules of grammar to say, "Take the hands out of the pockets", but that sentence would sound very strange to native English speakers. We're used to the convention that if you are talking about a person's own hands, you call them "your hands" or "her hands".
But a similar sentence using other objects might well not use possessives. "Take the food out of the microwave" or "Take the book out of the library" would not strike anyone as strange. You might say, "Take your food out of the microwave" if you want to make clear that it is the person's own food and not someone else's, or "Take the food of your microwave" if there is someone else's microwave in the vicinity. But that's normal use of the possessive: you use it when you want to make ownership clear, you don't use it if ownership is irrelevant, unknown, or if you want to de-emphasize it.
But any time you talk about body parts, you almost always identify whose: "your hand", "my foot", "Sally's face", etc. Only if you are speaking of body parts in general would you not identify who they belong to, like "The surgeon is skilled at operating on kidneys" or "The brain cannot comprehend such wonders". Even there, many general statements are made personal, like "This shampoo is good for your hair".
Ditto for clothes that people are wearing at the moment. If you said, "I spilled coffee on my shirt", we would normally understand that to mean the shirt you were wearing at the time. Similarly, "I spilled coffee on his shirt" would mean the shirt "he" was wearing. "I spilled coffee on a shirt" would normally mean a shirt that no one was wearing. (I say "normally", because in context you MIGHT mean a shirt owned by this person or that person but that they were not wearing at the time. But that would have to be called for by the context.)
Ditto for a person's home and car. English speakers say, "I painted my house yellow" if they mean their own house, not, "I painted the house yellow." Some people do refer to their own home as "the house" or "the apartment", but this is a rare usage.
You certainly can say, "Those comments are replies to comments I deleted" or "... to the ones I deleted". There's no need for a possessive there. Indeed, including the possessive makes the sentence look awkward to me. I'm not quite sure why. It's not that an adjective is inappropriate at that place. If you said, "Those comments are replied to old comments I deleted", or "... to irrelevant comments I deleted", the sentence flows fine. But "my comments I deleted" or "Bob's comments I deleted" sounds awkward to me. Anyone else here feel the same? Is there some rule this breaks?
