How to change colors of an imported image and remove specific parts of background

[bet_531]

I’m new to illustrator and think I might be searching using the wrong terms. I own a small crafting business and I purchase a lot of designs (.png) from Etsy however I generally need to modify the colors of certain parts of the images. I also need to send these images off for printing (UV DTF Decals, DTF Transfers, etc.) which require me to remove the backgrounds of the images. I have been able to view enough videos to get my desired output but I’m hoping there is a faster way or less steps being that I have to do this to several designs as I customize per order. 

This leads me to my two questions….

1. When I image trace, I always choose High Fidelity Photo but this brings back sometimes more than 60 colors. Is there no way to just click on the part of the image that I want to change the color of? Or someway to get back a smaller result without compromising my image?
2. When I need to remove the background of an image I always run into an issue with the insides of letters. When I attempt to delete the white space, it leaves the letter without the cutout part. How can I solve this issue?

Thank you in advance and please let me know if my needs would be handled better with say photoshop or another product.

51 colors returned but only 3 colors present

Letters before.....

Letters after I remove the inside...

[Monika Gause · Accepted solution]

You can use the Recolor artwork to reduce the number of colors in the design. You could also try and do that in Image Trace. WIth the setting Reduced number of colors and then move the slider.