It is difficult to find a complete set of 14 pieces from the heptominoes with any simple conditions. The following problems are from a set made by adding a domino to the P pentomino and removing concave pieces and those pieces with width two.
Another type of two-square problem this time with a rectangle made with multiple copies of two heptominoes.
If we combine a domino, a square and a 2x2 square we get a set of 21 pieces. These can form a 7x21 rectangle to form the basis of these problems.
These problems are based on constructions made with a single polyomino