The key is to separate [being polite] and [paying respect] to someone (the respectful verb form is called an "honorific" form). Being polite is always directed to person one is talking to. You use a polite from to another adult but not to a child. Paying respect can apply to the person you're speaking to or a third person you make reference to. Think of two equal British officials referring to the Queen as Her Majesty in their conversation. They are showing respect to someone they mention, independent of how formal or casual the conversation is. The sentence endings -ㅂ니다, -ㄴ다, -아/어(요) indicate politeness level, while the 시 verb suffix shows the speaker's respect for the person related to the verb (the subject). This person may be the conversation partner or it could be a third person referred to in the sentence. So there can be four cases: casual-ordinary, casual-honorific, polite-ordinary, polite-honorific. (A boy and his brother talking) 1) casual-ordinary: 네 친구는 어느 학교 다니니? (다니니? = 다니다 + -니? non-honorific) 2) casual-honorific: 아버지가 곧 오셔 (오셔 = 오시어 = 오시다 + -아/어 = honorific) (아버지 is not present, but they use an honorific verb when referring to him because he's their father) (Two adults talking - 영철 is the name of one person's son) 3) polite-ordinary: 영철이는 내년에 중학교(에) 가요? (가요 = 가다 + 요 = non-honorific) 4) polite-honorific: 장 선생님은 휴가를 언제 가세요? (가세요 = 가시다 + -아/어 + 요 = 가시어요 = honorific) When you converse with an adult, you talk like (4), with polite endings and using honorific verb to refer to the other person. So you'll say a lot of -세요 (-시어요) form which has these two attributes (e.g. 가세요, 하세요). If you're talking to a close friend, you drop the politeness suffix 요, and the verbs may or may not have the honorific 시 depending on who you're talking about (가, 해 or 가셔, 하셔). If you mention your pet in a sentence, you exclude the honorific 시 (가요, 해요). If you're telling your close friend about your pet, you drop both and use the simplest form 가, 해, etc.

You're right 시 is used both when talking about and talking directly to the person who needs more respect when talking about 사장님께서 오십니다 when talking to 사장님 이거 드시겠습니까? If you have to use polite expression, it is safe to use 세요 or 십니다 In fact, 요 and ㅂ니다 are usually used when you are talking with someone who is not close to you. It is very rare case to use 시 in conversations with friends It can be used in specific situation for fun For example you want friend to borrow money to you Then you can use 시 for begging 철수님 돈 좀 꿔주시겠습니까?