Problem # 1
I see some other logical error while selecting the components.
At the time of installation, click "Select all" at the bottom right corner. All the features boxes have single tick mark. Now, deselect only " Intel Threading building blocks" (TBB). Notice that "Intel C++ compiler" (ICC) box is still having tick mark without giving any warning. If TBB is required component for ICC then ICC should give warnings if TBB is not selected.
Problem #2 :
Try to modify the features where only intel C++ compiler is installed earlier using PSXE 2019 product installer. Select TBB in which both TBB core libraries for IA-32 and 64 are selected. Notice that Intel C++ compiler for IA-32 is disabled. Warning says ICC 64 or core libraries for IA-32. As I have already select core libraries for IA-32, ICC for IA-32 should be enabled. As of now, only if I select both ICC 64 and core libraries for IA-32, then only ICC for IA-32 is enabled.