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If "Rush Recklessly" is chained to the effect of "Blast Magician", and the ATK of the target monster is now higher than 700 x the number of Spell Counters removed, the effect of "Blast Magician" disappears. You cannot remove additional Spell Counters to increase the effect.
This is an effect that targets.
You must remove at least 1 Spell Counter. You cannot activate the effect and remove zero Spell Counters.
As with all Spell Counters, the Spell Counter is placed when the Spell Card resolves, not when it is activated, but "Blast Magician" must have been face-up on the field when the Spell Card was activated (and when it resolves) in order to receive a Spell Counter.
You place a Spell Counter on this card when the Spell Card resolves, so if "Magic Jammer" is used to negate the Spell Card's activation then you do not place a Spell Counter on this monster. But if "Imperial Order" is chained to the Spell Card, you still place a Spell Counter on this monster because the activation of the Spell Card was not negated. If the Spell Card was a Continuous, Equip, or Field Spell Card, and “Dust Tornado” is chained to its activation and destroys it before it resolves you still place a Spell Counter because the activation of the card was not negated.
"Blast Magician" must have been face-up on the field when the Spell Card was activated (and when it resolves) in order to receive a Spell Counter.