Buy a floor pump. You're getting into this bike thing and you should have one. Lots of opinions on these. I've gone through several over the years. My current pump is a Specialized Airtool Comp. It's lasted longer than most. 2nd, put your current pump in your spares box and buy a Road Morph. If you're using one of those pumps that comes with a water bottle bracket, the Morph should fit that bracket. If not, you might be able to get that sort of bracket from your LBS. The biggest problem with bike pumps is that vigorous pumping has a tendency to tear the valves out of tubes, which is probably what happened to yours. Deflating with the nut tight shouldn't tear the valve out. Floor pumps and the Road Morph solve that problem by connecting to the valves with a hose. Except when I use my deep aero wheels, I throw the nut away. You can get the pump on the valve just fine by pushing on the back of the valve with your thumb on the tire.

Some tires are designed to only roll one way. They'll have an arrow somewhere on the tire carcass. If you are using a cyclometer with a front wheel pickup, you'll have to move the magnet. Be sure to reverse the skewer so that the quick release is on the non-drive side. Got to look proper. Not to worry about the spokes. In any case, I don't think there is any advantage to be gained by flipping the wheel or reversing the tire's rotation. I've never felt the need to do so in many 10's of thousands of miles.

As long as I'm yakking, when you mount a tire, put the label over the valve, and on the skewer side. Then when you flat and are looking for what caused it, you'll know the orientation of the tire compared with the tube. Unfortunately, the latest style in tires is to put labels on both sides, total bummer. Idiots.