I'm confused about characteristic checks. Does a melee strike constitute a strength check? A spellcasting as an intelligence check?

The reason I ask is because I'm looking at the talent cards "Might Makes Right," "Coordinated Efforts," and "I Seem to Recall..." all of which give bonuses to their respective characteristics. Does that mean when I cast a spell, I can use "I Seem to Recall.."? When a dwarf troll slayer uses a melee attack, he can use "Might Makes Right" every time?

Yes. Provided the other restrictions on the card are adhered to, of course. (eg, Might Makes Right requires a fortune point to be used and ISTR ISTR exhausts the card)

Any time you base a pool on a characteristic score, that is a characteristic check.

It feels strange, because in many games, only a straight 'attribute' check would benefit from that kind of bonus, but it is explicitly stated in this game that any check that contains a characteristic as part of the pool constitutes a characteristic check.