What is the ruling on promising to abandon play until progress is made in da'wah (Islamic proselytizing/invitation), and is it considered an oath or a covenant? Do the lapses of the promiser invalidate this promise, or must it still be adhered to? And do the same rulings apply to someone who used the phrase "I covenant with Allah"?

Fulfilling a promise is a characteristic of believers, and breaking it is a characteristic of hypocrites. Fulfilling a promise to Allah Almighty is even more deserving, especially if the promise is to perform an act of obedience or abstain from a sin. A mere promise, if it does not include an oath by Allah, is not considered an oath and does not require expiation.

If a person says, "I covenant with Allah to do such and such," then Sheikh al-Islam leans towards it being a vow and an oath if the covenant is for an act of devotion and obedience. Slips do not nullify the promise; rather, one must continue.

As for the companion, he is obligated to fulfill what he covenanted with Allah. He is not subject to another expiation if he commits what he swore not to do, unless he swears a second oath, or the wording of his first oath implied repetition, or he intended by his oath the repetition of expiation with the repetition of the act he swore to abandon. Thus, once a breach occurs, the oath is dissolved. However, violating a prohibition incurs sin repeatedly with repeated violations.