I'm afraid that: sợ (là), e (là)

Sợ means "be afraid of": Em sợ chó. Before a whole sentence, usually with là, it means "I'm afraid that" or "I'm worried that": Đi sớm đi, em sợ là kẹt xe. Let's leave early, I'm worried there'll be traffic (in Hà Nội, tắc đường).

Like English "I'm afraid", it also softens bad news or a refusal: Em sợ là mai em không đi được. I'm afraid I can't make it tomorrow. The person comes first, and là can be left out, just as after nói or nghĩ.

E là means the same and sounds more careful, so it suits talking to a boss or a customer: Tôi e là dự án sẽ trễ hạn. I'm afraid the project will miss its deadline. E rằng is the written form, since rằng is the written "that". Ngại is gentler still, and usually means you hesitate so as not to trouble anyone: Em ngại làm phiền chị. I don't like to bother you.

Chắc (probably) makes a plain guess: Chắc ảnh không tới. He's probably not coming. Em sợ là ảnh không tới is the same guess, but you'd rather it weren't true. Biết đâu keeps a chance open, often a hopeful one, and liệu simply asks: Liệu ảnh có tới không? I wonder if he'll come.