I was wondering if switching between very different majors like humanities to a science major is usually difficult to do in universities like Brown, Boston, Chicago, etc.? Is switching schools within a university in general very hard to do? Also, is it hard to major in a field but also minor in a completely different field of study (i.e. major in computer engineering and minoring in English)?
As long as it does not involved switching schools within universities it is usually not difficult. But it is never a good idea to apply stating one major with the intent to switch for the purpose of, for example, applying to a less competitive major and then hoping to switch to a more competitive one. That is a well worn strategy which is usually made difficult becuse it often does involve switching schools (from liberal arts to engineering or business, for example).
Generally not difficult early on. There are exceptions e.g. if you are admitted to Penn Arts and Sciences it may be difficult to switch to Wharton.
Depends on the school and whether the destination major is oversubscribed there.
Even when there are no capacity limits, be aware that some majors have longer prerequisite sequences that need to be started early if you want to keep the option open to do them.
Most freshman do, in fact, change their majors. The question really is when you’re trying to change major (junior year is late for humanities into STEM) and how schools handle the declaration of major (for example at UCB you must declare your major by applying to that major).
And yes, many people minor is unrelated fields. I personally think it shows passion and breadth but others don’t share my opinion.