Yes, a simple pool test will suffice for now, and yes, you can use the agricultural lime to lime the pond.
Sending a water sample to be tested for alkalinity, pH, hardness among the other basic tests will give you a good baseline to start. Then a year later you can get another test done to see how the things that you did changed the water chemistry. In the meantime, a simple pool test kit can suffice. pH? 6.5-7.5 is ideal, 6.0-8.5 is the range. At either ends, you want to adjust the water to get it towards the ideal. Time of day matters when looking at pH if you don't have a lot of buffering capability in the pond. pH will be low in the morning and highest mid-day, then drop towards evening. That curve will flatten out when the buffering capability is increased. Less pH swings, less stress on the fish.