I am a native English speaker and this was difficult for me to answer. You are not alone! :-) Here's my best explanation: "Presume" and "assume" have similar definitions. They only differ in usage. When you're more confident about something, you can use "presume". When you're less confident about something and you're making a guess, you can use "assume". Examples: *I presume that you're bored, since you're looking at your phone. *I assume that you want to do something else. -In this example, when you say "presume", it's in a more confident way, drawing upon physical facts. Your friend is looking at their phone, and so you think that they are bored. When you "assume", you're not so sure and you don't mention a lot of detail. *I presume that it will rain tonight, since it's cloudy. *I assume that the weather won't be so great later. -Again, when you use "presume" you're more confident and you draw upon physical facts. When you use "assume", it's in a more vague context. Side note - in America, there is a funny saying: "when you assume you make an ass of you and me", since "assume" is spelled like 'ass', 'u', 'me'. It means that when you assume, you are making a poor decision without evidence. Usually, when you guess, it's like gambling and the outcome won't be great.

To presume means you can use logic to guess a result based on some facts or proof, while the possibility of "to assume" would be more slim.

In everyday English, not a lot. There is a subtle technical difference that may be relevant in legal contexts, but for most people they're interchangeable in sentences such as 'I presume/assume this is the right address.' Note that these verbs have other uses where they aren't interchangeable, for example 'assume a responsibility' or 'missing, presumed dead.'

Honestly, I think if you just used "assume" you would be fine in almost all cases. "Presume" has a more formal connotation.