Welcome to the wonderful world of cycling. I hope you have many happy and safe hours on your bike.
The best piece of advice I can give you comes from my wonderful BF. I hate hills though I must admit the dislike has diminished some. He told me often when we rode together "shift often" when approaching and climbing a hill. You basically have to anticipate the terrain. The goal is to maintain your cadence all the way up the hill (easier said then done, I know).
The issue with you chain is probably a result of you putting to much pressure on your pedals. Ease up just a bit as you shift and hopefully the problem will disappear.
Have a great ride!
Marcie



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