So I ordered this rechargeable lithium polymer ion battery for my LED strip, but the plug for the battery is male, and the plug to power my LED strip is male too. (My LED strip has 4 wires, 2 for connecting to a higher current, 2 for data from the Arduino) I ordered the battery for my wearable project because of this guide. I'm not sure how to recharge this, or how to connect it to my strip, should I just cut the male ends off and just solder the wires together?
make a double female extension or cut and splice or cut and crimp new female connectors... or cut and solder directly... anything that makes sense... I would caution solder if it's permanent and you do not have any way to recharge or replace.... connectors are good when it comes to batteries.
You need a LiPo battery charger for that. You can buy el-cheapo LiPo charger boards online. This is the one I always use: https://www.ebay.com/itm/264295129217 (no specific endorsement of that vendor - as always on ebay, the picture is usually the best way to identify which design you're ordering)
The connector on the addressable LEDs is probably also a different type of connector ("JST" is a company, they make hundreds of different connectors - unfortunately people talk about a "JST connector" as if it was a single type of connector). Wire up an adapter. You can buy connectors with wires on ebay, eg, the LiPo connector jst ph 2.0 | eBay. The LED strips usually use JST-SM connectors.
IIRC you can barely get decent blue out of a WS2812 at 3.7v - they're really meant to run on 5v. What I always did was use one of those "power bank" modules to power wearables (with a microUSB cable and an adapter wired up from one of those micro-usb breakout boards that's dirt cheap on ebay)