I don’t know about reading minds, but he certainly he certainly can interpret feelings well enough to know Leia is Luke’s sister, to sense fear, hatred, etc. It’s not so much of a stretch to believe he might have sensed whatever that rebel was holding in his hands was of great importance. Adding to that, the man frantically shouting “Take it!” before his demise, and the lenghts they went to protect that object might have been clue enough for him that he needed that tape.
As for his agility, he certainly isn’t doing backflips or the many nonesensical movements done in the prequels, but he is much slower in Empire. His ability to deflect blaster fire is present there, but he’s fighting one person (which he was expecting to appear), not an entire rebel batallion. I’d assume if he was able to fend of those troops he’d do it with greater difficulty, or in an entirely different manner.