be afraid to do　不敢，胆怯去做某事，是主观上的原因不去做，意为"怕"；
be afraid of doing　担心出现doing的状况、结果。 doing 是客观上造成的，意为"生怕，恐怕"。

She was afraid to step further in grass because she was afraid of being bitten by a snake.
她生怕被蛇咬着，而不敢在草丛中再走一步。
She was afraid to wake her husband.
她不敢去叫醒她丈夫。
She was afraid of waking her husband.
她生怕吵醒她丈夫。

go on to do　做了一件事后，接着做另一件事。
go on doing　继续做原来做的事。

After he had finished his maths，he went on to do his physics.
做完数学后，他接着去做物理。
Go on doing the other exercise after you have finished this one.
作完这个练习后，接着做其他的练习

interested to do　对做某事感兴趣，想了解某事。
interested in doing　对某种想法感兴趣，doing 通常为想法。

I shall be interested to know what happens.
我很想知道发生了什么事。 (想了解)
I'm interested in working in Switzerland. Do you have any idea about that?
我对在瑞士工作感兴趣。你想过这事吗?　(一种想法)