My cat usually starts yelling whenever he wants something, though it is near impossible to tell if he wants to play "chase" or wants pettings or is hungry. What I want to ask is whether I can teach my cat to touch certain objects in my room depending on what he wants, like touching the bed if he wants petting or touching the drawer if he wants to play "chase" and so on? For reference, my cat is 4 years old at the moment, so I know that I might be a bit late to start training him.
Yes, you can teach your cat to show you what he wants. However, it will take some time and the cat is not the only one that is learning in this situation.
The age of the cat is not important for the learning; they do learn all their life. However, some cats are better in giving you the visual signs of what they want than others.
As an example on how a cat can show you what it wants: my cat is sitting looking out of the window, and she jumps down and comes to me, does the head bumping, she takes a few steps away from me, and she lays down waiting for me.
As soon as I get up, she starts walking to the door so I know she wants to go outside.
All cats give you signs of what they want, but some are better than others in doing this. And you, the owner, need to pay attention to what your cat is signaling to you to get the message.
When communicating with your cat be consistent and try to use short words or sentences. I use the words "show me what you want" when my cat talks to me, and the cat I have now is not as good in doing this as my previous cat was. In conclusion, there are some differences in different cats in how good they are in communicating what they want.