It depends a ton on who you're watching. DJs can do a lot or a little, and you can play sets which are much more pre-planned or much more improvised. Scratch turntable players can turn a record into a musical instrument in its own right, of course, but I'll assume you're mainly asking about dance music.

If you go to a big stadium EDM show, you'll see a lot more DJs sticking very closely to a script and playing the songs in a predefined order with transitions at pre-planned times - often these are planned to coincide with visuals and lighting cues. For huge audiovisual productions with a lot of moving parts, the fewer surprises the better. But if you go to an underground venue or an ordinary nightclub, you'll see a lot more DJs making their song selections on the fly, based on the mood of the room. and the reactions on the dance floor.

Generally, yes, they're mixing the songs. What this means is that two or more songs are playing back on different turntables or decks, and the DJ is adjusting the pitch and tempo of their playback so the songs will sync up and sound cohesive together. Usually they're also making EQ (equalizer) adjustments, to emphasize or kill the highs or lows in a song, so that the bassline of this song doesn't crowd out the low end of that one, or things like that.