1. There isn't a difference. Note that 'elder' is usually only used for family relationships between people, usually brothers or sisters. 'Older' can be used for anything - a book, a car...anything at all. 2. The difference is not necessarily one of politeness. 'Older' and 'elderly' are both polite, but they imply a different age groups. 'Older people' is quite a vague term. It might mean 'senior citizens' (60+), but you could also refer to people in their 40s or 50s as being 'older people', depending on your perspective and the context. 'Elderly' implies a much older age group - someone in their late 70s, 80s or 90s. 'Elderly' might be a polite word, but a healthy active 65 year old would be extremely insulted to be referred to as 'elderly'!

For me I prefer to say "older brother" not "elder brother". "Elder brother" sounds a bit old-fashioned to my ear, but depends on regional and personal preferences (I am from London, and I don't have any brothers btw!). On the other hand "eldest brother" seems more natural to me than "oldest brother". Elderly people to me means very old people, i.e. they cannot walk very easily and are a bit frail/weak. Older people to me means anyone over 65, they might be very healthy and active! I hope that helps!

Two other observations about q1: 1. Pronunciation: It is slightly easier to flow the 'y' of 'my' into the 'e' of elder than the 'o' of 'older, but this can be overridden by personal preference. As there is also more regional variation in pronunciation in British English, it can depend on your location in the UK as to which version you would hear more. 2. Implication by use: both adjectives are comparatives that have associated superlatives: 'oldest' and 'eldest'. While grammatically possible to use 'oldest brother', you would more often use and hear 'eldest brother'. Hence, when using 'elder brother', the speaker may be implying that they also have an 'eldest brother' too, whereas when using 'older brother' there is less likelihood that the speaker is implying that another more senior male sibling exists. I should make it clear that this is a very subtle distinction and few, in any, misunderstandings would be created by substituting one adjective for the other.

1. You can say either. I would usually say older brother/sister. 2. Elderly people is more polite :)