It all depends on the dish you are making mirch. You can put pomegranate seeds in pakoras but for chanay, you need to grind them. You cant put khatai powder in liquid daal or it will turn out dark brownish. Tomatoes wont give the sour flavor to every dish. SO contingency.
Depends on what you are preparing, but for the most part, no.
Think of it this way, all of these ingredients taste different. Tatri adds a very different flavour if you compare it to fresh lime juice, or vinegar or aamchur, or anardaana.
If you need to add something tart to your meal, and dont have the recommended ingredient, you can always substitute-- just dont expect the same flavours.
Lemon with vinegar, and aamchur with anaardana are somewhat interchangeable, but again, depends on what you are making.