You say you are importing the logo into FH and it looks like crap. But you also said the logo was made in FH 1O. You didn't make the logo yourself, I assume. Are you in FHMX when you 'import' said logo - how does that work, anyway? If it's a native FH format and it's specific to a recent version of FreeHand, you simply open it, not 'import' it.
Also, check your preferences for the set resolution you can view raster images with. You can view placed / raster objects at high rez for optimum clarity or you can go all the way to the other end of the spectrum, which entails crude-looking image files that load fast because the preview is low-rez.
The other bit you mentioned about breaking apart the text is interesting. Are you talking about live, editable text, or text that's been turned into curves - vector objects? If the former, you may have a corrupt font issue. Otherwise I'm having a tough time following what you mean.
Finally, your question about ensuring that vector objects are nicely anti-aliased pertains to how you export a native FH file into a rasterized format. You do have some control over the degree of anti-aliasing possible in .jpgs. Beyond that, recent versions of Illustrator have AA built in, so you could export a FH 10 or MX file to an AI 10 file and open it up in Illustrator and it would indeed have the AA features. Earlier versions of both these apps were not able to handle AA, so anything you bring into them will of course look relatively jagged.