Is the rate of photosynthesis higher than the rate of respiration?
The net exchange of gasses in any area will be different depending on the number of plants and what plants they are.  This is because it depends on the number and size of leaves, and because chlorophyll is essential for photosynthesis, it also depends on the amount of chlorophyll in the leaves. Therefore that part of the question is very broad.

Overall, photosynthesis (oxygen production) is higher than the rate of respiration in plants during a year.

Aerobic respiration continues all the time in plant cells (in light and in darkness), using up oxygen and making carbon dioxide. Photosynthesis, in contrast, occurs only in light and uses up carbon dioxide and makes oxygen. The more light there is, the more oxygen is produced.

There is a light intensity at which respiration and photosynthesis cancel each other out. This is called the compensation point. Below this level carbohydrates are used up and the plant cannot grow.



This and more can be read in this document from the Royal Society of Chemistry