So, the coins counter, aka score, is at the top right. The combo is on the puck, it's an important number because most of the strategy is about increasing it and catching the extra coins that fall. I agree that it's not the best place to put it on desktop, but there are fewer options on mobile. I'll see how it feels to put it at the top, or even replace the score with just the combo display.
You start with just one life by the way, but if you pick up more they'll be shown as hearts at the top right near your score.