Mycoplasma stands out among bacteria for one reason above all: it has no cell wall. Almost every unusual fact about it traces back to that single feature. Let's test each option against this.
Three of the four statements follow directly from the lack of a cell wall. Beta-lactam sensitivity is the one exception, since a drug that targets wall building cannot work on an organism that has no wall.
Let's summarize:
The false statement is that Mycoplasma is sensitive to beta-lactam antibiotics.