I would not cut them off. While they may not be aesthetically pleasing to you, the plant is still using them to make food. Let the plant shed them if and when it chooses to.

besides, by the looks of it, if you cut those leaves off, it doesn't leave many on the tree

The brown spots are from over watering and/or salt build ups.

Tell us how you water, how often and what you use as your tell to ensure the soil is dry enough to water again.

What type of soil are you using and does the pot have a drain hole?

Thank you for your advice! I am new to fiddle fig trees.

I water ever second week or so. I live in Los Angeles, and the weather is starting to get in the 90s though. I usually just stick my finger into the soil about one inch, and if it is bone dry, I water with 1.5 cups of water. Every other month, I include one drop (literally) of "SuperThrive Vitamin Solution," which seems to really help the plant.

I have had the tree for 6 months, and it is still in the original soil from the store. There is a drain hole in the bottom of the pot.

Thank you in advance!

Soil moisture management is critical for plants, and it's one of the most common things we tend to get wrong. Plants like their soil moist, not wet, so our job is to learn how to make that happen so the roots get the oxygen and living conditions to function properly.

Here's a post by Al that's all about how to deal with troubled plants. The end of the post is in the first reply to the OP, so keep going.... It can seem dense, but absorb as much as you can, because all that stuff will turn into tools you can use in all sorts of plant-related situations.

It takes almost no time at all to check soil moisture, and your ficus will love the improvement in growing conditions. Rather than blather on I'm going to cheat a little and give you a quote from a post by tapla (Al) about watering:

"You can tell you've watered too much (or too little - the response is the same - a drought response) when leaves start to turn yellow or you begin to see nutritional deficiencies created by poor root metabolism (usually N and Ca are first evident). You can prevent overwatering by A) testing the soil deep in the container with a wood dowel ... wet & cool - do not water, dry - water. B) feeling the wick & only watering when it's dry C) feel the soil at the drain hole & only water when it feels dry there.

Soils feel dry to our touch when they still have 40-45% moisture content. Plants, however, can still extract water from soils until they dry down to about 25-30%, so there is still around a 15% cushion that plants can still absorb considerable moisture after soils first feel dry to us.

Water slowly until the soil is saturated but no water (or very little water) has exited the pot drain. Wait 10-15 minutes and water again so at least 15-20% of the volume of water used ion both applications flushes out the accumulating salts. After the pot stops draining, you can return it to its normal spot and arrangmt. Wait until time to water again & repeat the routine."

Another thing: if the soil is water retentive, you can remove excess water that would otherwise saturate soil at the bottom of the pot and kill roots in that area.

After the pot is finished draining, by prop the pot up at a 45 degree angle for about 15 minutes, then return it to the normal position. If the drain hole is in the middle you'll see some more water come out. Repeat until no more excess water appears.