You can say farmorsfar, mormorsmor etc, but notice the little S that appear between the second and third part of the word.
Another word is gammel + farmor/mormor/farfar/morfar, e.g. This term is ambiguous though, as it's not entirely clear exactly whose morfar he is. Is it the morfar of your parent or your own morfar's parent? Usually context will tell though.
A more normal translation in British English would be "Grandfather likes fish with lemon." (I typed this in and was informed it was incorrect.)
Oh Sweden, you're so optimistic. "Tycker om" directly (word-for-word) translates you "thinks if" (or "thinks of" if you want to refine it a bit), even though it means "like." In the direct translation, you are assuming that you like someone when you think about them, meaning that if you don't like someone, you just don't think about them.
"Tycker om" doesn't mean "think of" in the sense of just thinking about someone, it means "think of" in the sense of having an opinion about something. If I had to hazard a guess, I'd say it had something to do with how you can "think well of" something, but that's purely a guess on my part.
The main translation, as you can see above, is Grandfather likes fish and lemon. Both in Swedish and in English, if you just say Farfar or Grandfather, we will assume that you are talking about your own one. In English, they tend to use my a bit more often than we would in Swedish, so that's also an accepted answer. But the grandfather isn't a natural way of speaking about your own grandfather in English, and the Swedish sentence doesn't have him in the determinate form either, so that answer cannot be accepted.
The machine picks from all accepted answers and shows you the one it thinks is closest to what you input.
I was luckier today: I translated Är hon hennes mormor? as Is she her grandmother? and it was accepted, although I was told that "another correct solution" would be Is she her grandmother? ;-)