Is 害怕 only used in the literal sense of "be afraid of, be scared", meaning "to be afraid of snakes", etc. and 恐怕, on the other Hand, for abstract worries? and can 怕 be used in both senses?
The context in which I would use 恐怕 is something similar to "I'm worried this might be the case". I'd say it is used to describe a predicition or extrapolation, sometimes can be translated to be just "probably".
- 這池恐怕有三公尺深 : The pool here is probably 3 meter deep (and that worries me)
- 我恐怕會被留校 : I guess I'm going to be in detention
怕 alone can be translated to "be afraid of":
- 我怕蛇 : I am afriad of snakes
- 我怕高 : I am afraid of height
... or "be weak against / be bad at"
- 我怕燙 : I'm weak against hot (food/drink)
- 我怕冷 : I'm weak against cold (weather)
... or "being a chicken and not willing to face it".
害怕 is more of a mental state and perhaps less of a verb. If it is, it's probably a intranstive verb.
- 我對這裡的交通感到害怕 : I feel scared by the traffic here
- 這電影院令人害怕 : The movie theather make me scared
The use of "害" usually implies "bad effect".
Now... there could be use cases in which 害怕 and 恐怕 are shortend to be just 怕. In this sense, perhaps 怕 is more abstract than the other two. In summary:
- 區別的方法只怕很難說明 : Describing how to disambiguate is probably going to be difficult.
online dictionaries have the answer (note example phrases): bkrs: 怕：动
（害怕; 畏惧） fear; dread; be afraid of:不怕疲劳
不怕任何困难 怕得要命 狼特别怕火 没有什么可怕的。 （担心） be afraid of; have a fear of; for fear; fear lest:她怕把孩子吵醒 我怕打扰你而没有来拜访你 副 （也许，表示估计） I'm afraid; I suppose; perhaps:会议怕要延期了 事情怕不这么简单
害怕to be afraid to be scared 因遇到危险、困难而畏惧或发慌。害怕得要命 她不再害怕他们会误解她了 这小女孩非常害怕打雷
恐怕(1) [I'm afraid]∶表示估计并担心
(2) [perhaps; maybe]∶表示估计, 相当于"大概"、 "也许" 天气那么热, 恐怕就要下雨了 他们恐怕需要我们的帮助 恐怕他是忘了
much more including English at bkrs