What about weather? When planning a cross country, I'm guessing the day of the flight you might need to either reroute some, but also during the flight may run into weather that you need to go around.
I'm guessing that could involve (specially for use newcomers) some fancy calculating, while flying?
Do CFIs usually wait until clear days, or figure this is all part of it, when the weather is slight, not dangerous but requiring some changes in th plan?
Not only will the CFI go over weather with the student, it's mandatory.
That said, stuff changes. I literally got weathered out of my home airport on my solo long XC by a thunderstorm that was isolated but far too big to go around. I landed and called the CFI from an airport 50 miles away saying I was on the ground, airplane was safe, and a mutual friend of ours had offered to let me crash on his couch.
CFI handled letting the rental place know, said they had all been watching this oddball storm pop up along my route, and were concerned about it, and that the decision to land was the correct one.
Called him in the morning to go over the plan to finish the XC the next morning, continued the flight, and had the airplane back only 1/2 hour late for the next person on the schedule. Rental place had explained what happened and the student and CFI that were scheduled were more than gracious about it.
The route of flight was only GXY to EIK that was left. The entire rest of the XC was done.
Adding to the problem was the lateness of the hour, which made circumnavigating the thunderstorm before dark, problematic. No night privileges at that time, of course. Probably still be legally "day" but I wasn't comfortable with it, and couldn't really see how far back that storm went, or whether there was another one right behind it.
Keep in mind this is in the day when radar weather was available at airports, but only on the terminal inside and you waited for it to come down over a 56K modem on a noisy phone line. No iPad or mobile data to land and take a peek at the radar picture.
The "calculating" wasn't a problem, by that stage, and shouldn't be. Figuring out how to go around it wasn't the problem, it was the time needed to do so.
Which has also led to the joke from him over the years that I'm the guy who can literally find the only cloud in the sky for hundreds of miles, and it'll be right in my way.
Thankfully this hasn't been that true overall, but I've landed just to look at a weather chart or radar loop (versus calling up Flight Service or Flightwatch back then, which also worked, but you couldn't see it for yourself) more than a few times in the logbook, back in those days, after I had the Private rating and was buzzing around the prairie. That was just how you updated your weather picture in your head if something wasn't looking right. You didn't have many other options.
I remember when I saw my first laptop with charting software on it and a very expensive XM weather receiver hooked to it and just had to have one. That company was the one that eventually went full-retard and sued everyone saying they created the magenta line.
After running that stuff on a regular laptop for a while, I bought some crazy semi-tablet thing the size of a dump truck and dragged that around with the borrowed XM receiver from a friend. Thing had like a half hour worth of battery and had to be plugged into ship's power to actually use it for an XC, but it was pretty cool compared to landing to look at a weather chart!