When is the 把 construction forbidden?
Simply put, 把 is just used to denote the object.

However, the object particle 把 can only be used when the action is done entirely on the object and the object undergoes some consequences or changes after the action. This also implies that the object is doomed to experience the consequence once the action is triggered. 

For example, the following sentence will be very wrong: 

我把汉语学习。 = I learn Chinese. (?) -> wrong 

Here, "学习" means learn. Object particle is not used here as "Chinese" itself did not undergo any consequences or changes. Unless you use the completion form 了, then it will be OK to do that as "Chinese" has been in your mind deeply (did have some kinds of change), otherwise it will be unnatural to use the object particle. 

So, in your example above, the use of 把 is correct in each of the four sentences. 

OK, so the only problem left is whether the four sentences are natural or not to be spoken.

Bear in mind that Chinese loves simplicity. So, for the particle 把，you should use it only when it is important that the listener does not miss the object (i. e. 笔 in your example).

Correct me if I am wrong.