So i did all the missions, drifting with a wheel was the most excrutiating thing ever, i think years of drifting with a controller on NFSU and NFSU2 have ruined me, but i eventually got there, i haven't tried drifting on a controller in GT7 yet but in GT Sport i did it with a controller for the trophy and missions if there were any and it was relatively easily for me.
The Human Comedy guides were quite useful for "anticipating" the weather, and jumping from slicks to full wet back to slicks is the best way to make time on the races with rain.
Honestly i found the tsukuba one the hardest with a winning margin of just 17 seconds, i think i messed up the pit strategy a bit and saved too much fuel and didn't need to extend the stints because the rain would eventually come, the refuel rate is quite fast so burn it up if you need to.
Followed by Alcase winning by 22 seconds but that's because i used a z28, that sambabus was hard to keep up with at times.
I thought autopolis would be hard as i couldn't get the lead until after the second pitstop, i saved a little bit of fuel which turned out to be great as the refuel rate is quite slow and the front runners burn through almost a full tank, ended up winning by 46 seconds but it was a stressful first 2 stints.
I have a theory that the AI is running something similar to B spec in GT5 where your B spec driver can get hot and cold depending on if they are battling or not and their temperament stat because once i cleared a gap to gallo in tsukuba after the second shorter pit stop i pulled away very easiliy.
Another thing that might help those that don't find these missions so easy is that you should read what the "pros" have to say at the race setup screen, eg: lucas odonez says his sambabus had an engine swap, others might tell you what pit strategy they're on, and so on.