.) This sounds about right. I'm trying to remember Itachi's exact timeline off the top of my head. He opened his Sharingan around 8-10 or a little earlier, and graduated from the academy at 8 I think, and finally he made ANBU Black OPS captain at 13 from Kakashi. Minato would've been sealed in the Shinigami before all of that. Maybe he saw him at recess like Hiruzen did, lol. We know that on the night of Madara's 2nd attack with the Kyuubi, Itachi was taking care of baby Sasuke, 16 years ago.
All someone needs to do is not be lazy like us and do a little addition/subtraction of birth years, lol. 
That'll take about 5 minutes or less to look things up and less than a minute to do the arithmetic in your head.
There's only a few ways I see them interacting and that's before Minato was Hokage (I'm sure he was highly influential before being Hokage and it opens the timeline a bit, albeit make Itachi even younger, lol), or while Hokage during the 3rd ninja war and shortly after, since we know that they both went through the war and it changed Itachi.
2.) Minato as the supposed "destined child" seems to have a way with words, based on his passing words with "A" the Raikage about Bee. Whatever the experience was, it was only something brief like this, there was no elongated relationship. It seems like a few passing sincere words from Minato can go a long way, and maybe Itachi got some. I think that's a large part of what makes someone a "destined child" candidate in Jiraiya's eyes, Possibly Itachi just watched him from a distance to understand roads to peace, his and Minato's.
2b.) Still, I think Minato left an impression on Itachi based on the speech Itachi gave Naruto in the last chapter or if that was just Itachi understanding his own successes and mistakes, or some combination thereof. Itachi is a genius, and I believe he could understand a person like Minato very well without ever interacting with him directly, he may have admired him or simply studied him as a person trying to achieve the same thing,
peace, by a different means and comparing their success to see which method was better and what road to follow. Clearly, based on Itachi's speech and burning Shisui's eye with Ameratsu, Itachi has made that decision. While he's still a lone dog for the most part, facing Kabuto alone, he's entrusting things to others such as Sasuke to Naruto, Naruto to Bee, Naruto's friends to Naruto and vice versa.
P.S. Really, the fact that Itachi trusted Naruto at all with Shisui's eye, seems to me an indicator that he was already moving away from his lifelong direction of doing everything himself. I see no reason, he couldn't have programmed the crow with Shisui's MS eye genjutsu for Sasuke's 3-tomoe Sharingan unless Madara could simply dispel it. However, I'm not sure how Madara would know it's there, as while the Sharingan can see chakra and chakra flow disturbed under genjutsu (see Kakashi gaiden, when Obito recognizes Rin in this state, Shisui's MS genjutsu Kotoamatsukami is on a whole different level than some rock chuunin/jounin, and we only know that a doujutsu of greater insight, Ao's Byakuugan could see it used by Danzou. That doesn't mean the Sharingan can't, it just makes me wonder if it couldn't.
Apologies, a bit off topic.).
Side note: While with Itachi and Minato it's hard to do, but I have more respect for Itachi in the latest chapter for his speech to Naruto. Not only did Itachi understand Naruto, but he seems to have understood himself, Minato, and many others, even if it took him being brought back from the dead for extra time to figure out the right path. I just hope he can rest in peace when this is all over.
Apologies for the long reply, I just started writing and kept going, feel free to pass over if you're not interested.
Peace
