Is $$x=7$$?
>(1) $${x}^{2} \lt 49$$
>(2) $$x+y=13$$

Correct.
Plug in 7 for $$x$$. Then $$7^2$$ is not smaller than 49, so $$x$$ may not assume the value of 7. Remember that the statements are to be considered as facts, and so Plugging In values have to comply with the statements. In this case, $$x$$ cannot be 7, so **(1) No → Sufficient → AD**.
Statement (2) introduces $$y$$, an alien from outer space. We have no knowledge of $$y$$. Yet, it influences the value of $$x$$. So $$x$$ may be 7 if $$y$$ is 6, but it can also be anything else. So **(2) Maybe → Insufficient → A**.

Incorrect.
Because $$y$$ can be any number you can think of, so can $$x$$.

Incorrect.
Combining the statements isn't necessary to answer the question stem.

Incorrect.

Incorrect.

Statement (1) ALONE is sufficient, but Statement (2) alone is not sufficient to answer the question asked.

Statement (2) ALONE is sufficient, but Statement (1) alone is not sufficient to answer the question asked.

BOTH Statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.

EACH statement ALONE is sufficient to answer the question asked.

Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.