As Fly said, the MOST important thing to fix first or locate first is where the water is coming from.
The most likely point of leakage will be the keel bolts. The H22 has very few thru-hulls where water can come in. Other than the keel bolt holes, the only wetted hole is the sink thru-hull. Any others would have been done by the p/o. It is possible to replace and or seal the keel bolts without taking the H22 out of the water. But if you have a trailer, that would be the easiest.
From experience yes 2 1/2 inches of water in the bilge is a lot, its about 7 gallons of water, in one day. Although I have had as much as 50 gallons. I know, because at the time I had to pump the water into a 5 gallon bucket, and then pour it out.
The only place you can put any standard kind of bilge pump is opening under the steps. I have a Rule 1100 manual/automatic pump that when I was having problems put there. I then ran the discharge line up and out of the companion way and drained into the cockpit. The problem with placing the pump here, is its not the lowest point of the bilge, so it never gets all the water out. If you search this site there are some pics where and owner ran some (what looks like) pvc down the sides of the keel trunk to the lowest point (where the keel bolts are), but still put the pump under the steps. I tried that too, but couldnt get enough suction to get the pump going.