Hmm, not really. 1. Today I have had a very saturated day. We wouldn't say this. Do you mean a very full day? 2. I'll hold the lectures. It's not clear what this means.

2. For this one, I need you to describe the context of the sentence for me. I am unsure what you are trying to say. The sentence makes sense grammatically but I don't know what it means.

1. You would not use "saturated" in this context. You also don't need "have AND had" for the past perfect here. "Have" is unnecessary. If you were trying to say you had a lot going on during the day, you would say, "Today, I had a very busy day."

Yeah. The first one is correct but it sounds a little odd. You might want to say "satisfying day instead" if youre trying to say that you had a beautiful day. Second one is correct too.