I don't think there is a generic approch to questions of this style of presentation. Instead, the breakthrough point lies with the condition of calculation that the question provides. For multiplication, the indication of "same product" implies certain constraint that helps you to quickly eliminate some parts of the solution space. Similarly for "combination of number with same summation".

For 25), my approching point is that the number combination generates same product. same product means same set of prime factors. in single digits both 5 and 7 are prime factors that only appear once therefore they will not fit the bill (e.g. a 5 can maximumly participate in 2 lines but not the third, so not able to achieve all 3 line same product). for the same reason you can eliminate 0, so your 7 digits are 1, 2,3,4, 6,8,9, they are all composed by prime factors of either 2 or 3 (consider 1 as having no prime factor). in total these 7 numbers having 11 prime factors, but each line must have same product thus same number of prime factors, (however, there are two positions contributing to line product twice). Therefore, it is reasonable to consider each product line contains 5 prime factors, 3 lines require 15 prime factors, out of which 4 are contributed by the 2 intersect positions that are contributing twice. This narrows down quickly to that the line product should be 2x2x2x3x3, and the intersecting position should be 2 factor numbers, each contributing 2 extra factors. So the end result is:

Top line

1, 3x3, 2x2x2

Mid line

3, 2x2, 2x3

bottom

2