5e - Quick questions about premade adventures from WotC.

Hey guys, I haven't been able to find an answer through googling so I'll ask here.

Are the adventures (OotA, RoT, PotA, etc.) continuous? If so, what's the order? I've heard some conflicting information and want to clear things up.

Also, how flexible are these adventures in terms of improv around the campaign? I'm a new DM looking for something to do after we finish LMoP. Still not decided if I want to jump into one of these modules or flesh out a home brew campaign. I'm thinking long term with this group.

Thanks