As a note, you should never use the "MoveObjects On" cheat on sims. It can cause issues in your game rather rapidly. Using the MoveObjects On cheat (or MOO, for short) is not a great idea to use on any sim objects that can be interacted with (i.e. tables, stoves, beds, etc) as it can cause a lot of issues with your game when sims try to use them, even if they have space.
In some people's games, using MOO even a little, can cause lag and freezing. unfortunately, my games have always had issues with the building cheats. Other people though, seem to have little issue with it being used in their games. I think most people tend to fall in between. In general, it is best to save MOO for items that won't be interacted with like landscaping plants and such.
From what I have read, the biggest issue with MOO is that it is a Sims 2 tool that was adapted to work in Sims 3, but not made for it. So it is a kind of use-at-your-own-risk type thing.
As for the Culinary career, there is no beginning level site for the career path. If you had walked your sim down to the Bistro and had them get their job there, they would have started out at level one there. I think it is random when you use the newspaper or computer. You should be able to take your sim to the Bistro and switch their job to that rabbithole. If not and you are still low-level in the career, there really isn't much point to not just quitting one and then going to get it at the other if you still want to delete the Diner.
The lot placement with the arrows only happens in Edit Town when you are placing a lot from there. By picking up the Diner in Edit Town and trying to place it back down, you would be 'placing it' so you would get the arrows. The arrows only really do anything though if you are placing a smaller lot onto a bigger one though.
For example, say you really like your sim's starting house and want to move it to a bigger lot so you'll have a bigger yard... now you can pick up your lot in Edit Town (with the Move Lot option/the hand) and place it on a bigger lot. For a long time, this meant your old lot would end up right in the middle of the empty, bigger lot. Now with the arrows though, you can move your home lot onto the bigger lot and then adjust where it sits on the lot. This helps if say you want the room for a pool in the back or a big front lawn, and so forth.
With the Diner the arrows would not help because you would be placing down the same sized lot. However picking the lot up and then placing it back down in Edit Town would have evicted everyone off that lot and onto the sidewalk around the Diner lot, where hopefully they would not be stuck any more.
The school stuck sim issue is not the same as the issue where sims used to get caught on commercial lots. On the school lot they get 'caught' because too many sims are trying to enter into the rabbithole at once, so in this case, adding a second school and replacing the original (to reset it) would help because it would split the students up between the schools.
The issue with sims stuck on commercial lots that used to happen a lot (I am pretty sure it was patched at some point) was not because sims couldn't enter or exit the rabbithole, they would just all get 'stuck' there where as far as you could see there was nothing in the way or any reason to be stuck. They would often stay there until they died.
Since you said that your sims were stuck because of the air conditioner, then that isn't exactly the same thing either. The only place that I have seen this issue is in the newer world Roaring Heights, because of the pier. The solution there was to move the diner or delete the air conditioner. If the air conditioner in question is not a separate unit then, the only option to retain the Diner would be to move the Diner while in build/buy mode. That would require that you move any objects in the way first (like tables, trashcans, and such) then moving the Diner rabbithole itself a little forward. You might have to use MOO to be able to place it down again. Just make sure when you put the other objects back in place that you leave enough room for sims to use/interact with them and to enter/exit the building without route failure or getting stuck. And always remember to turn off MOO when you are done with it or it can cause issues!
I second the advice to not expect everything to be like the Sims 2, it is a lot different. The guide site linked for you above is a good place to start.
Also, keep in mind that Sims 3 is a VERY glitchy game, many of the bugs and issues from years ago are still not fixed. Many people have to use Twallan's Overwatch and Error Trap mods to be able to play their games without them becoming corrupt and/or lagfests, as they attempt to fix/work around so many of the unfixed issues and bugs.
I had so many issues with CC/mods in Sims 2 that I swore off them when I started playing Sims 3. But at some point I had to start modding my game just to be able to keep playing. Thankfully, Twallan is such a good modder and I've never had any issues with his mods except when I did not update them to my current patch level.
Good Luck!
