Answer to: Where to order pebble steel Battery replacementI don't think so. The Pebble Time products have completely different chassis dimensions and motherboard shap; I believe they're thinner for example. The chassis dimensions and motherboard shape affect how much space there is for the battery. There are teardowns for the Pebble Time products; you should look at those to get some idea. You might have to disassemble your Pebble Time and use calipers to measure your existing battery. If you do that, please add that info to the relevant teardown article specific to your product. Also note which Pebble Time product you have. The Time Round, Time Steel, and Time (plastic chassis) are all different external dimensions and most likely have different batteries.
Answer to: Where to order pebble steel Battery replacementI didn't need to solder. The connector on board is fine, but it's just friction (and a piece of foam glued to the back) that keeps the cable seated in the connector. So my tearing was just the cable partially unseating. I never had the classic, but my issue was intermittent and for a while I was convinced rebooting the watch made a difference; kinda seemed to. There's forum threads that claim memory leak causes the tearing.