I filed Turbo-tax online in 2022 and used the desktop versions in 2023 and 2024. I need to amend 2022 and 2023, can I do all those on my latest(2024) desktop version?

No, you cannot use the 2024 version to prepare or amend any years other than 2024.  In order to amend those older years, you'll need to do this on the 2022 and 2023 Desktop versions.

See:  How do I amend my federal tax return for a prior year?