Does Training Grounds reduce the cost of level up costs such as Beastbreaker of Bala Ged? Thus reducing the level up cost to only 1 green mana in this instance?
Yes, level up is an activated ability so training grounds will reduce it's mana cost. In your example it would indeed only cost G to level up the creature.
Yes. The Level up keyword ability denotes an activated ability.
702.85. Level Up
702.85a Level up is an activated ability. "Level up [cost]" means "[Cost]: Put a level counter on this permanent. Activate this ability only any time you could cast a sorcery."
702.85b Each card printed with a level up ability is known as a leveler card. It has a nonstandard layout and includes two level symbols that are themselves keyword abilities. See rule 710, "Leveler Cards."
Thanks in advance!
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