When I change gearing I just have to get used to the new ratios. Upshift later, downshift sooner, and when putting along in 1st-gear, either put along faster or -- if it's a tricky trail -- slip the clutch a little.
The sprocket should have zero side-to-side play on the countershaft. The chain on the sprocket should have a little play although not much.
It's a little hard to parse what you're writing with no punctuation, no capitals, and several subjects mixed together. You may get answers faster if you type slower.