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DivinylsFan  The newspaper should be delivered near the front door, but there may not be space for it on the porch, especially if there are stairs and maybe another object or two.  Also keep in mind that the game doesn't always consider a door to be a front door; see whether you can set it as such.  As an example, a door to a room with a toilet cannot be set as (or considered to be) a front door.

I've moved the front door when gradually building a large house, and the newspaper delivery shifted as soon as I manually set the new front door and without my doing anything else.  But these doors were also no more than ten squares from the street, in case that makes a difference.

For the carpool, the first one seems to be set behind the mailbox, as if there were a line running from the mailbox towards the street and that became the front border of some invisible parking space.  However, a second or third carpool, or a school bus, will get pushed back from there, either by the first carpool car or by another vehicle (cleaning, repair, food truck, etc.) that parks on the street.

It's also possible that the "front of the lot" determines where the cars start parking.  You can set that with the testingcheatsenabled true cheat, by ctrl-shift-clicking the ground and selecting that as the front.  You'll see an arrow pointing to the "front," and I'm not sure whether it matters exactly where that arrow is.  I haven't tested, but you can yourself if you're curious.

None of this has anything to do with where your sims' cars' parking spaces are.  I've had them anywhere, and nowhere at all, and the carpool doesn't move.

DivinylsFan  I was saying the carpool slots don't move, only the newspaper delivery.  Try the set as front of lot cheat to see whether it helps.  Even though you're setting the same side of the lot as the front, the exact placement of the arrow might help... or it might not, I don't know.  Or you could set a different side as the front and switch back, this time clicking the ground on the far right.

For the newspaper delivery, can you set/unset that one door as a front door?  If not, the game doesn't see it as an eligible door, maybe because of the shower.  You could try putting the shower in inventory to see whether that's the issue.