Does VHDL have a ternary operator?

No. It was discussed for VHDL-2008, but didn't get in. You've got a couple of options. If your tools support VHDL-2008, conditional assignments are now supported as sequential statements (they were previously just concurrent), so you can write something like:

process(clock)
begin
  if rising_edge(clock) then
    q <= '0' when reset else d; -- ie. much like q <= reset? '0':d;
  end if;
end process;

If you haven't got 2008, just write a function (q <= sel(reset, '0', d)). You have to write it for every type you're interested in, though.

Not the one like you know from C/C++ but you can use:

destination <= signal1 when condition else signal2;