Is it obligatory to straighten the back in standing, bowing (rukuʿ), prostration (sujud), and during the tashahhud? Does the prayer become invalid by bending during the standing position or by not straightening the back during the tashahhud? And what is the explanation of the hadith: "There is no prayer for one who does not straighten his spine"?

A slight curvature of the back while standing, bowing (ruku'), or prostrating (sujud) does not invalidate the prayer. The important thing is that the worshipper does not go beyond what is considered "standing," and is not closer to bowing. What is sufficient in bowing is that the hands reach the knees. As for its perfection, it is for the worshipper to grasp their knees, straighten their back, keep their head level with their back, and raise their forearms. What is obligatory in bowing is for the worshipper to be closer to a complete bow, such that it is recognized that they are bowing. In prostration, the worshipper should be upright, raise their back, and not hunch. Curving the back during the tashahhud does not cause harm. The hadith "A man's prayer is not valid until he straightens his back in bowing and prostration" indicates the obligation of maintaining stillness (ṭuma'nīnah) in both, and that abandoning it invalidates the prayer according to the majority of scholars.