Gremmi: Free roam is back as DLC in the form of Jimmy's Vendetta (which is closer to the Free Ride Extreme mode of the original).
As for bonus/side missions and the like, they were originally supposed to be in the game (you can talk to several NPCs who just always say 'I haven't got anything for you right now', and a telephone system exists but you're always told you don't have any numbers to ring) but were cut for unknown reasons. Whether it's so they can sell it to you as DLC later or simply for pacing reasons (the game itself is ostensibly not free-roaming, it's a linear game that happens to have an open city) we'll never truly know.
there is third possibility - those things (sidemissions, melee weapons, etc) while they had them somewhat done, probably were not completely polished up to 100%. And 2K simply wanted to release the game to get some of its money back, so everything that was not completely finished and polished got cut, even if it was almost done.
It would be nice if they released the missing stuff for free, kind of like CDP with EE on Witcher, but sadly this is 2K.. so they will charge for it.
And me, sucker that I am, will buy it, because I love Mafia 1 and 2 and want to support 2K Czech, even if their publisher and owner now sucks ass.