Just how old is Nishi? According to The Other Wiki the film takes place in 1994, and Nishi appears to be in his sixties, maybe seventy at the most. He claims to have studied in Germany "before the war" and fell in love with that woman. Yet in the flashbacks showing how he first found the Baron the costumes do not look anything like 1930s fashion - if anything they look like something from the years prior to WWI. It could be that the artists were taking liberties, but it does not seem plausible that he could be old enough to have done the things he claimed to have done.
Let him be born a bit before 1920 - 20, 21 as he left Germany, around 75 in the movie. He opens or closes the shop depending on his mood, so it's a retirement hobby at this point, and he doesn't find it all that easy to move around anymore as far as I can see - Shizuku had to help him with the stepladder. I saw nothing out of the ordinary for a guy in his seventies. As for the clothing in the flashback, it's probably part artistic choice, part mirroring the dolls themselves (which are most probably a good bit older than the 1930s).
The clothing makes sense once you realize that this scene isn't a true flashback so much as Shizuku's visualization of the e events as they are told to her.
Does Seiji speak Italian? If not, how did he get by in Italy for 2 months? And if so, has he been learning Italian just so he can go to Italy?
Well, violin-making is his passion. So it's possible that he decided to learn Italian early on. It's also possible that the master in Italy speaks Japanese, considering that he's a friend of Nishi.
Just how old are Seiji's parents? His father was "Dr." Amasawa when he donated the book to the school's library in 1953 (according to the English subtitle translation of the flyleaf), 41 years before the story occurs. Whether a medical doctor or an academic, he was unlikely to be less than 23 when he gave the book. That puts him at least age 64; but by having a much younger wife Seiji's age is quite possible. Surely he can't be any older than that or tongues wagging would have ensured that everyone in the school knew who Seiji was (the guy with the ancient father). For biological reasons it is not credible for his mother to be that elderly, but because Seiji's last name is not Nishi, she is presumably Mr. Nishi's daughter. Nish is argued above to be roughly 75. Presuming Nishi was still single when he returned to search for Louise after the war, which would have been a daunting prospect until at least 1950, and that searching took him a year, he ends up marrying earliest at 1952, age 33 or so, and can have a girl child soon after. So Seiji's mother is born 1953-60, marries Amasawa any where from 1971 to 1978, then has Seiji in 1979. So Seiji's parents are father 64 (min) and mother 34-41. Some would say lucky Dr. Amasawa.
What happened to Nishi's wife (Seiji's grandmother)? Nishi doesn't noticeably miss her. Louise is who is in his mind, and there is no suggestion that he travelled back to Japan from Germany with an illegitimate child in tow.