Can a rocky planet (like earth) be larger than a star? If not, why
not? Can a star start out as a planet (a non-gaseous one like earth)
and then grow so large as it accretes more mass that it actually turns
into a star when nuclear fusion ignites?

As an object gets larger, it becomes more and more able to capture and
hold gases which move quickly (hydrogen and helium).  Once they can be
held, because they are the vast majority of matter, you could keep
accumulating them until you form a star.  Of course, if something else
nearby becomes a star first, it's quite likely to blow away all the
other gas around when it ignites.  The outer planets formed where
temperatures (and therefore the speeds of hydrogen/helium atoms) were
low, so it was easier for them to grow by grabbing the nearby gas. 
Earth and the inner planets got too warm while they were too small to
hold on to these gases.

Hope that helps. No charge ;-)

First part: yes.  Consider the case of a neutron star - it may be as
small as 30km in diameter.  Something more Earth-like?  How about
white dwarves - approximately the same size.

Second part: probably.  Consider Jupiter - a wannabe star if ever
there was one.  It radiates more energy than it receives from the sun.
 Let it accrete a bit more gas, and who knows.

Cool question BTW.

If we define a star as being capable of sustained nuclear fusion, the
minimum mass is about 80 times that of Jupiter (I'm ignoring brown
dwarfs since they can't sustain fusion). This is equivalent to more
than 25,000 Earth masses. The size, however, wouldn't be much more
than Jupiter, which is a bit over 1400 times the volume of Earth. So,
making the huge assumption that a rocky planet that size wouldn't
collapse under its own gravity, you could have a rocky planet larger
than a star.

I'll guess no for the 2nd question, on the grounds that there wouldn't
be enough material laying around to be accreted. Once fusion starts in
a star the solar wind does a pretty good job of blowing away anything
that's not already a sizeable lump.

Ian G.