Single Table Select With Aggregate Function

I'm probably not seeing the obvious so I keep making the same mistake. The
table holds water chemistry data from multiple streams, sites within each
stream, sampling dates, and many chemical constituents.

What I need to do are three things:

1.) Find the date and site for the maximum value of a specified constituent
on a named stream.

2.) Find the values of that same constituent at other sites on the named
stream on that same date.

3.) Find the date of the maximum value of a constituent for all sites on
the named stream.

Thinking the last the easiest to do, I submitted this query:

select max(quant), site, sampdate from chemistry where stream = 'SheepCrk'
and param = 'TDS' group by site, sampdate;

but this gives me the value of each site and date, not the maximum for all
dates at a specific site. Postgres tells me that both site and sampdate must
be in the 'group by' clause.

Obviously the syntax is more complex than I thought it would be and I
would like a pointer to the correct way to write these queries.

Rich