I think I understand your question. In the cases you list, you can't remove the "some" and still have those phrases be correct. I'll give you an example: A) I did some shopping today! B) I did shopping today! In that case, A is correct, and B is not. You would have to rephrase B, and say something like "I went shopping today!". However, with a few verbs, you could take out the "some." There are not many cases when you could. Another example: A) I did some laundry today. B) I did laundry today. A & B are both correct in that example. This is an exception though!

I did some shopping. I did the shopping. I did a lot of shopping. After "do" you require some kind of article. You can use the zero article in the following: My new robot is good. It does shopping, it does ironing, it can do cleaning, etc.

If you take out "some" in those sentences, it sounds wrong. You can say "I will go shopping." or "I'm going to go shopping." or "I'm going to shop." As for the other sentences, "I'm going to read" or "I will read." "I'm going to hike." or "I'm going to go hiking." or "I'll go hiking." Those are just some other ways to correctly say the example sentences you provided.