Unfortunately there is no pattern that I'm aware of. You just have to learn the words. What complicates it even more is that some words are spelt differently depending on the English speaking country. In the US for example "centre" tends to be spelt as "center", whereas here in Australia and the UK it is "centre".

Sorry, no. It does depend on etymology, but sometimes even that is obscure. Sorry. English is certainly an adventure. You never know what to find around the next corner!

-er and -or are suffixes that create a noun from a verb. Usually, the noun represents a person or machine that performs the action of the verb. -er is most common. A teacher is someone who teaches. A baker is someone who bakes. A copier is a machine that copies documents. -or is less common. An auditor is someone who audits. More information here: https://www.thefreedictionary.com/Commonly-Confused-Suffixes-er-or-ar.htm

As others have already answered, searching for rules or patterns in English spelling is a futile task. As already noted, one complication is the differences between American English and English English. But also, given that you can argue that English is essentially a mix of German and French, at least in the roots of its spelling (or you might say Anglo-Saxon and Norman, to give it some historical context), you can see where some of the more crazy spellings come from. For instance, compare "night" with the German "nacht" and it starts to make a bit more sense.