In any events after Harry had his first lesson with Snape, was there any record of him using anything he'd learnt in one of the lessons successfully?
Harry was able to close his mind off from Voldemort when he experienced grief (e.g. after Dobby died) but it's unclear whether that counts as a real Occlumency.
His scar burned, but he was master of the pain, he felt it, yet was apart from it. He had learned control at last, learned to shut his mind to Voldemort, the very thing Dumbledore had wanted him to learn from Snape. Just as Voldemort had not been able to possess Harry while Harry was consumed with grief for Sirius, so his thoughts could not penetrate Harry now while he mourned Dobby. Grief, it seemed, drove Voldemort out... though Dumbledore, of course, would have said that it was love. (Deathly Hallows, Chapter 24: The Wandmaker)
There were no cases when he successfully used Occlumency other than grief-influenced immunity, either with Snape during practice or Voldemort.
Nobody tried to Legilimency on Harry aside from those two in the books (discounting Sorting Hat in books 1/2).
No, because he has the dreams and visions throughout 5 and there's never a line like 'he tried to not see what he was seeing and it worked' or anything to that extent.
He manages to stop Snape from seeing more of his memories at one moment in their lessons but it's implied that he was too emotional. Page 534, chapter Occlumency. Snape says:
'Did you mean to produce a stinging hex?' (There's an 'angry weal' like a 'scorch mark' on his wrist.)
'No,' said Harry bitterly, getting up from the floor.
'I thought not,' said Snape, watching him closely. 'You let me get in too far. You lost control.'
Then page 636 he tries to practice during classes:
'but it was no good, hermione kept asking him what was wrong whenever he fell silent trying to rid himself of all thought and emotion and, after all, the best moment to empty his brain was not while teachers were firing review questions at the class.'
(This is their OWL year so there is a lot of review.)
But, there is a moment during one of there lessons where he uses a shield charm that protects himself from having memories revealed, but then he starts to see shape's memories. Snape says something like
'I don't remember telling you to use a shield charm but there is no doubt that it was effective.'