得 as a verb particle can be used as:
potential particle (to express possibility or capability)
There are only two potential particles. They are '得'(able) and '不'(unable)
做得來(can do) - 做不來 (can't do)
看得清(can see clearly) - 看不清(can't see clearly)
resultative/degree particle (to indicate the result or degree)
做得有聲有色 - [做(verb)+ 得(resultative particle)+ 有聲有色 (result/ degree)
打得他頭破血流 - [打(verb)+ 得(resultative particle)+ 他頭破血流 (result/ degree)
'他' in "我打得他頭破血流" is the object of the phrase
You can replace 他 with any object, for example, "打得約翰頭破血流"
'到' is another resultative particle, as in "打到他頭破血流"
but in 2. I'm not sure. It seems more like 使得 is just 'make, cause'.
'使' already indicates 'cause', '得' is redundant if you just want a [cause phrase + effect phrase] structure; - [使他 (cause him to)][闭上眼睛，心理就有竹子的影子]is enough
in [使得 (verb + resultative particle)] [他闭上眼睛，心理就有竹子的影子 (result)]
'得' indicates the result or degree of the verb "使"(make); and "他闭上眼睛, 心理就有竹子的影子" is the result or degree of the verb.
The reason why '得' here is redundant when the verb is '使':
"使(得)他闭上眼睛，心理就有竹子的影子" = [(cause)+ (to the degree of) + (someone to became/ to do something)] can be expressed without the resultative particle '得'
As in "使他闭上眼睛，心理就有竹子的影子" = [(cause) + (someone to become/ to do something)]