Is it okay to hook up a battery Charger to charge my battery without removing it?

That's how it is normally done. Leave the cables connected to the battery. Attach the charger's cables, red / positive to the battery's positive post, and negative to negative. Way too often we read that someone connected something backward and caused a real lot of expensive problems. There's a big + molded into the battery's cover right next to the positive cable, and a big minus sign next to the negative cable.

Turn the charger on after its cables are connected to the battery. It is always better to charge at the slowest rate the charger offers. This is more important with older batteries. Home chargers vibrate the battery's plates which hastens its eventual failure. The slower the charging rate, (current), the less the plates vibrate.

Take a peek at this article too in case I overlooked something:

https://www.2carpros.com/articles/how-to-charge-your-car-battery

Happy to help. To expand on my wondrous knowledge, the positive post is always larger in diameter, but it isn't practical to run around measuring them when the plus and minus signs are right there. You wouldn't believe how many people connect jumper cables and battery cables backward. That's why I always mention it. Years ago it was also common to see red paint on top of the positive terminal and green paint on the negative. Today it's more common to find red and black plastic caps on the posts. Those get thrown away, then their usefulness is gone.

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