I had a quick look at the interface and it should be fairly easy to hide those two elements with CSS.
This is how the character count for the question code is implemented (I still believe this is a good feature because it shows you the limit of the length of the codes, but hey, whatever floats your boat...
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):
So you basically would need to hide the CSS class "typeCounter--container". This should get rid of the character counter (not tested!).
And her the code for the Question types.
This might require a little bit more of testing because I don't know if the class "small" is used in other occasions (I would think so). So you might have to specify the ID of the DIV it is in maybe. To avoid that it disappears on other occasions. My guess would be that it is "accordion_question_type_selector_QuestionSelect-128". What irritates me is the 128 at the end. Not sure what this stands for and if there are various of these with different numbers at the end. You would have to test this.
Now you need to check where the CSS files for the admin interface themes are and either create your own theme (might not work anymore after some updates that impact the admin themes) or adapt an existing one (chances that it gets overwritten with updates).
As I said, I personally don't think that these features (you might see them rather as "bugs") will concern anyone for more than 2 seconds.
But I think I have shown you an option on how to hide these two things.