I'm afraid we're going to need more information about your coins to provide meaningful answers.
"Australian Olympic equestrian coins" - I assume you mean the aluminium-bronze $5 coin. It's worth more than "face value" - they were sold at $9 each and the book value is around $15. Alternatively, you could mean the little medal they were selling with a badge.
I'm afraid there is no such thing as a "silver 1983 American quarter". Even the ones sold in proof sets were not silver between 1965 and 1992. If it looks silver (check the rim; non-silver US quarters look like a "sandwich" with silvery cupronickel outside a pure copper core), then it's probably been silver plated by someone after it left the mint.
Australia has issued a large number of different kinds of "five dollar Australian coin", including the Olympics ones mentioned above. But the most commonly encountered one is the Parliament House $5 from 1988. These are extremely cheap and common; they were sold at face value through the Commonwealth Bank, and the plastic wrappers the Bank sold many of them in caused them to discolour. Pristine examples may be worth a few dollars more, but discoloured ones are onl worth face value.
"NSW royal mint $10 uncirculated 1987 coin" - These "state series" $10 coins never really caught on with collectors, and are rarely worth much over bullion value. Current BV is around $18; don't expect much above $20 for it.
"1993 royal Melbourne show $1 dollar coin" - I think that's the one listed in the catalogues for $9.
