These probes are available from many commercial sources, but this company site give a very nice overview: https://www.thermofisher.com/us/en/home/references/molecular-probes-the-handbook/assays-for-cell-viability-proliferation-and-function/assays-for-apoptosis.html
TUNEL staining for apoptosis and LC3B staining for autophagy are very commonly used. These can be fluorecence or non-fluor, like immunoperoxidase.
There is a comprehensive guideline for autophagy monitoring published in PubMed. Please check it in following link:
https://pubmed.ncbi.nlm.nih.gov/33634751/
If confocal microscope is available for your institute, LC3 immunofluorescent staining is a common method for alternatively monitoring autophagy. Others, if autophagy is a key factor for your investigation, autophagy inhibitors (bafilomycin A, 3-methyladenine) might offset your treatment and which could be direct evidence for incidence of autophagy.