First of all, yes. Squatting is an invaluable part of growing in the scope of lifting. And the issues you are experiencing, have long-standing workarounds ready and available for you.
You mention balance. This is something that will come with practice. Right now, the problem is most likely related to the fact that you're not used to carrying weight in this manner. Unless there is some underlying reason, it should come naturally and organically.
As for ankle mobility, this is usually a case of your tendons being too short, or too stiff. Neither case should hinder you from doing squats. We have quite a few different ways of doing squats, and some people tend to one or the other simply based on what their body can most easily cope with. Here are some examples:
The back squat
Bar on your shoulder/neck. This is where people often will realize that their ankle mobility is a limiting factor. You will notice, because as your knees bend, your heels come off the ground. This is not ideal, because the force should propagate through your heels and into the ground. Your heels are, after all, where your legs meet your foot.
Try placing your heels on a slight elevation. Most people use weight plates for this. It should allow you to keep more weight on your heels, rather than at the balls of your feet, near the toes. Even so, it's more of a temporary fix.
Spread your feet a bit further, and point your toes slightly outward. I see a lot of people miss this key point. They have their feet shoulder width apart, and toes pointing straight forward. I have excellent ankle mobility, and if I try to do this, I will also lift my heels off the floor. It's a terrible way to do it.
An excellent way to find a decent foot placement, is to pretend you're about to take a dump in the woods. Squat down, and make sure you're not about to get anything on your legs, but maintain balance at all times. This will often result in a wider-than-shoulder-width stance. Kind of like riding a horse. Again, toes slightly outward.
This will allow you to lean back more, so that the weight isn't tipping you forward off your heels.
The front squat
This is where I found my personal workaround. With the front squat, you have the bar on your shoulders, but on the front-side of your neck. Yes, it is trickier, but mastering this squat will help you.
I find this extremely useful for those who have ankle mobility issues, because with the weight already on the front-side of your center of gravity, you will have to lean backwards onto your heels in order to not tip forward.
One hopefully minor setback here, is that it takes some getting used to. A lot of people simply hold the weight wrong.
The right way: With the bar resting on your shoulders, close to your neck, your elbows should be pointing straight out in front of you.
The wrong way: You'll notice a lot of people having their elbows pointing down, and the bar resting 50/50 on their shoulders and hands. Their wrists will be bent backwards with tremendous force, and they'll spend most of the exercise, and rest periods, in pain, squeezing their wrists.
You, on the other hand, will know better. Hell, with your elbows out in front of you, you don't even need to use your hands. You can cross your arms over the bar for stabilization if you need to. As long as your elbows are up high, the bar isn't going anywhere. But again, it takes some getting used to, and you will probably have to drop some weight.
Also thoracic extension (the good arch in the lower back area) will come very naturally when you front squat.
The overhead squat
My personal mount everest. Holding the bar over your head with your arms fully extended, you squat. This is one hell of an exercise in balance and mobility. Again, thoracic extension will be forced upon you, which makes it pretty amazing, but it's definitely a more advanced squat if you intend to work with it beyond simply testing the waters.
Another thing I like about it, is that you will absolutely be using far less weight with this one. Not only because you have to press/jerk it up, but also because keeping balance during descent and ascent is pretty challenging.
I would definitely test it out if the bar alone feels comfortable enough. If not, wait a while. There's no rush with this one. There's always the workarounds and the front squat for starters.
I've purposefully left out illustrations in this post, because it became quite long as is, and huge posts can be slightly off-putting. But there is a plethora of guides, tips, and tricks with everything I've mentioned, by simply googling the headlines. And there's always the comment section if there are any other questions.