I'm not to that point yet, but I'm wondering if when the main storyline finishes, will we get to free roam?

I don't imagine there will be much to do, but we can keep working on our settlements if we want.

As far as I know after X ingame days there will always be respawn of enemies at certain locations, so technically you can always shoot&loot and build. Dont know why that should stop after completing the story.

I've completed the story and I can confirm that you can still explore, build settlements, clear "dungeons", loot, etc. There is no "hard ending".

Well as much I know once you end the main history you will have quest popup, also its possible for you to have missed great side history quest, companions or settlement quest and achieving the end game, also there are the time based quest, and also there are faction specific quest, when you go with one factions the other became unavailable, so you can make a new character or keep going with the one you already make I usually do like 4 or 5 characters before I get to see the full spectrum of the history.

There's actually quite a bit of respawning in this game, more than I would have expected. Some places have the same enemies with the same hidden loot in the same numbers every time. Sometimes it's nice if you are gathering things, but other times it's just a pain - like where are all these enemies coming from? One would think that as we're going through and destroying all these enemy bases eventually the bad guy population would diminish. At the very least they wouldn't keep putting the same weapons in the same pipes.

Something about it just doesn't feel genuine.

Yes like outside that clothing store in Lexington, everytime i have gone back to it the missile launcher has respawned in a pipe outside the building, must have collected half a dozen of the things.

That is not, what 'open ended' means, but yes, you can continue playing after finishing the main quest.