You can treat the rhombus like it is 2 separate triangles. You know the base and height of one of the triangles, so you can multiply 1/2*10*13 to get the size of one triangle, which would be 65. BUT, you have to double that since you have two triangles. This gives you a total area of 130 square units.
To find angle SRQ, you use that angle TQR is 23 degrees. Since it is a rhombus, angle TQP is the same 23 degrees making the angle RQP a total of 46 degrees. Since angle RQP is 46 degrees, angle RSP has to be 46 degrees. Add these two together to get a total of 92 degrees. Then subtract 92 from 360 to get 268, which tells us how much is left over for both SRQ and SPQ. Divide 268 by 2 to get 134 degrees for angle SRQ.