Is it a hard instrument to play?

Yes and no. Hard on the fingers initially, but it is a very straight forward and logical instrument. If you already know a bit of violin, a lot of your knowledge is directly transferable. It is played with a pick and playing simple melodies and chords is a matter of a few weeks. To develop a good tremolo or complicated rhythmic patterns may take a bit of time, but can be accomplished with a regular routine of practice.

I already play the violin. How different is this instrument?

The mandolin is tuned exactly the same as a violin. Everything you play on a violin is immediately transferable to the mandolin. The clef you read is the same. The pitches are the same as well the neck size is similar. There are some differences such as using a pick instead of a bow.  Holding the mandolin on your lap instead of on your shoulder and playing between frets. There is a learning curve, but it is a really small one to overcome.

I heard someone say that F-style mandolins are better to play. What is that?

An F-Style mandolin is a florentine model. Essentially it is the same as the other shape (teardrop or A-style) but it usually has much better wood these days and it is decorated with scrolls and more ornamentation, thus the use of the word florentine. In the author’s opinion, yes it is better if you can get one, but the A-style is a very good model used by millions around the world.