Can a triangle have side lengths 2 and 3 and 7?

Answer 1

No it cannot. Follow the triangle-side rule:

a + b > c

In your case:

2 + 3 > 7 No

3 + 7 > 2 Yes

2 + 7 > 3 Yes

Since one equation is false, your side lengths are wrong.

Answer 2

No.

If two sides of a triangle are 2 units and 3 units long, the longest the other side can possibly be is 5 units long (in which case it's a degenerate triangle).