We present several advancements in search-type problems for fleets of mobile agents operating in two dimensions under the wireless model. Potential hidden target locations are equidistant from a central point, forming either a unit-radius disk (infinite possible locations) or regular polygons (finite possible locations) inscribed in a unit-radius disk. Building and extending on the foundational disk evacuation problem [23], the disk priority evacuation problem with k Servants [21, 27], and the disk w-weighted search problem [49], we make improvements on several fronts. First, we establish new upper and lower bounds for the n-gon priority evacuation problem with 1 Servant for \(n \le 13\) , and for \(n_k\) -gons with \(k=2, 3, 4\) Servants, where \(n_2 \le 11\) , \(n_3 \le 9\) , and \(n_4 \le 10\) , offering tight or nearly tight bounds. The only previous results known were a tight upper bound for \(k=1\) and \(n=6\) in [27] and lower bounds for \(k=1\) and \(n \le 9\) in [49]. Second, our work improves the best lower bound known for the disk priority evacuation problem with \(k=1\) Servant from 4.46798 to 4.64666 and for \(k=2\) Servants from 3.6307 of [27] to 3.65332. Third, we improve the best lower bounds known for the disk w-weighted group search problem, significantly reducing the gap between the best upper and lower bounds for w values where the gap was largest. These improvements are based on nearly tight upper and lower bounds for the 11-gon and 12-gon w-weighted evacuation problems, while the previous study of [49] was limited only to lower bounds and only to 7-gons.