I just bought rick dangerous on itch, using android phone, how exactly do I play/use the game. Do I need a pc to play it or is there any other option

In the downloads section of the game, there is a list of files. If it lists Android (the symbol) as one of them, then you can use Android. If there is a Windows logo, you can use Windows and so on for Mac (Apple logo) and Linux.

When you download it (assumming it's for Android), you should get a .apk file. Navigate to it in your file explorer (or equivalent) and press on it (and then follow all "are you sure" prompts). Then it will be added to your applications.

Windows: same but you probably get a bunch of files in a compressed format (.zip usually). Put the folder anywhere you'd like and right click -> extract all (select your destination). Navigate to the chosen destination and double-click the .exe file (Important! Keep all the files together in one folder!).

I'm the wrong person to ask for Mac and Linux, but it's probably roughly the same process as Windows (with different file extensions: Mac is .app and Linux is .86x_64 or .bin or .elf or something else which you have to look up).

Hope this answers your question