An ability that triggers "whenever you tap a creature for mana" triggers only if you activate a mana ability of a creature including {T} in its cost. Mana abilities that don't include the {T} symbol and instead say "Tap an untapped creature you control" or similar won't cause Leyline of Abundance's second ability to trigger. Similarly, it won't trigger if you tap a creature to activate a mana ability of another object (even if that mana ability also includes {T}).

A player's "opening hand" is the hand of cards the player has after all players have taken mulligans. If players have any cards in hand that allow actions to be taken with them from a player's opening hand, the starting player takes all such actions first in any order, followed by each other player in turn order. Then the first turn begins.