To identify an unknown led I would first look at it’s base dimensions to narrow it down and then try to match the die and dome. Here is a reference page with all the leds. A multimeter will not tell you anything.
For soldering I like the KSGER plug in models (not battery) that use the tips with the heater and temp sensor built in. Like this model. It’s about $45 plus you can get a lot of different tips for not much money. They heat up super fast, like 6 seconds and have accurate temperatures (accurate enough). You can also get a stand and a tip cleaner pretty cheap as well. I did a video of those parts here. There are a lot of good soldering videos on YouTube. Having a good iron, flux, solder, tip cleaner, etc makes a big difference to the results. These quick heating tips are able to feedback temperatures very quickly so when you go to solder on something with large mass and it pulls a lot of the heat out of the tip it can sense it and dump heat back in quickly so you get predictable results. Its way better than the older style soldering irons with replaceable tips.