Could I use a front rim to build a rear wheel?

Yes, but, it's a lot of work and you should consider whether it is cheaper/easier to buy a rear wheel already built.

Wheel building is a skilled job and does require tools most people don't own and or wouldn't be cost effective to purchase for a one off wheel build, which I can only assume this is. Not to mention the fact that if op does not know whether it is possible to build a wheel up as a front or rear shows they are not trained in wheel building. That's no big deal. Most people couldn't build a wheel myself included.

So basically don't get in to a specialised job if you lack basic knowledge. In simple terms wheels are available cheaply online, ready built by a trained specialist. This is a far easier and cost effective solution than buying all the tools and parts then learning to build a wheel.

In the days before factory built wheelset, rims where produced without being specifically for front or rear wheels. On most general-use standard bicycles it is still that way. The only difference was the spoke-hole count.

But many rear wheel rims today are no longer symmetrical, meaning the right side is different from the left. This is mainly due to the fact that with 11 or even 12 speed cassettes the dish of the wheel is very unsymmetrical and the angle at which the spokes reach the rim makes the spokes puts a lot of pull on the rim. This is being countered by positioning the spoke holes differently for the drive or non-drive side.

Although 36 holes was and still is the normal count on most bicycles, you could build wheels with 32 or 28 spokes, those being mostly used on front wheels, mostly for weight saving or aerodynamics.

Nowadays many rims are specialised for their use and designed for front or rear wheels in mind, mostly for aerodynamic or load bearing abilities and often with different spoke counts. Although with the advent of disc brakes the spoke count on many front wheels is on the rise. Disc brakes put about the same stress on front wheel as the drive puts on the rear.

But if you use one of the many 'standard' rims that are still in production, you may build a rear or front wheel with any rim.

Side-note: In the old days also front wheels would be built with thinner often double-butted spokes (1.5-1.2-1.5mm), while rear wheels had thicker (2mm) straight spokes.

Yes, with standard wheels the front and rear rims are identical. Just make sure the number of spoke holes of the rim matches your rear hub. Sometimes they use fewer spokes on the front. Some manufacturers offer asymmetric rims for the rear wheel (because a rear hub with cassette is inherently asymmetric) but you could still use a normal, symmetric rim.

Some proprietary wheel sets have other asymmetries and complex lacing patterns, but I assume you are not asking about one of those.

Yes you can if the rims themselves are both symmetric.

And, give it a try. Don't listen to the nay-sayers. Some people are so risk averse, I'm surprised they leave their houses in the morning.

What's the worst that could happen? This isn't amputating your leg. It's just a wheel. Bust a spoke? $2/each. Have to buy a spoke wrench? $10 used. Over tighten/strip a spoke nipple $0.50 for a new one.

You have to really try to damage the hub, or the rim. If it doesn't work, then take it all apart and try again, or work it 90% of the way and then take it to the LBS and let them 'true' the wheel for $20. You'll have learned something. You'll be more confident when out on your bike. You'll know what to do if you're on the trail and a buddy has a loose spoke. All good things, now you know something more about this great hobby, and that makes it more fun.