"The exact mechanism for tremor induction by β(2)-adrenergic agonists is still unknown, but there is some evidence that β(2)-adrenergic agonists act directly on muscle... More recently, tremor has been correlated closely with hypokalaemia." - NIH publication
First Aid mentions hyperthyroidism causing tremor from β-adrenergic stimulation. It also mentions β2-agonists causing tremor as a side effect. First Aid also mentions β2-agonists driving potassium into cells, which may contribute to tremor. That said, more classic symptoms of hypokalemia are wide QRS and peaked T waves on ECG, arrhythmias, and muscle weakness.
Looking around on the internet looks like if therapy is continued the tremor from a β2-agonists resolves overtime.
This probably isn't 100% politically correct but:
Beta 2 agonist is still a beta agonist so it can bind nonspeficially and cause B1 activation which will cause tremor aka activates general sympathetics.
Sweating is generally can be categorized as sympathetic activation but the sweat gland has a muscarinic receptor so it won't be affected by a beta agonist.
the remaining choices are parasympathetic responses.
The way I thought about it was a little more simplistic. We use non selective beta blockers (e.g. Propranolol) for the treatment of essential tremor. Therefore a beta agonist would have the opposite effect, aka cause or enhance tremor.
Plus, all the other options are not associated with B2 agonist, so just by process of elimination, tremor is the only one left
Albuterol - relaxes bronchial smooth muscle (short acting β2-agonist). For acute exacerbations. Can cause tremor, arrhythmia.