@Peaches Lee has a good response, I'll add some of my own experience:
1. What is the cheapest option for fencing?
Good fencing is WAY cheaper than a vet bill, or multiple vet bills, or having to put a horse down. We went with a field fence with small holes at the bottom. A field fence with a few strands of hot wire will be good, DO NOT get the bare wire New Zealand fencing, I've seen two horses get caught in it and neither lived, I've heard plenty of other stories of horses getting sliced open with it too. Also avoid barbed wire foe horses. Fencing is expensive.
2. How much (roughly) does food cost per year if it has a field to graze?
We are feeding about 1 ton per horse every 6 weeks with a half acre pasture per horse.
3. IYO what’s the best horse breeds for beginners?
There isn't a best breed, it's going to depend on the individual horse, typically stay away hot bloods (thoroughbred, Arab, Akhal Tekes). Depending on what you are wanting to do with them, a good QH can do a lot, if you're doing trail riding some gaited horses are nice. Your purchasing budget will factor in here, depending on your location a good broke horse can be 5k or more very easily, 10k to 15k would not be crazy from what I've seen lately. A grade horse that is reasonably broke for trail rising might be 2k or less.
4. Do they HAVE to have a stall? Or can they just be in a pasture 24/7? Also, blanket on cold days, or no? (Ik everyone has different opinions.)
Shelter for shade and to get out of the wind and bad weather. Horses are robust and don't require a stall to be locked in, unless you have one on stall rest.
5. What age horse typically has the best temperament? (I do not want an horse older than 15 since I plan on keeping it forever.)
Temperament is going to be more genetically based than anything and also how they've been handled. Any spoiled horse will be dangerous to you no matter how old they are.
6. The age old question, mare, gelding, or stallion? People say mares are always moody. Is that true?
Absolutely NO STALLIONS!!! Leave those to the crazy horse people who've been around them forever. Mares are not moody, some are just more opinionated than others, they have all their hormones. Geldings can be more agreeable, but not always. Again, this totally depends on the horse.
7. Which is better? Mule or horse? (IYO)
For a beginner, horse. I love mules, people say they are stubborn, they aren't exactly. If you think of a mule as highly self preserving, and you have to prove that they can trust you, and that they should take a step or stop or turn without coming to harm. I've ridden some awesome mules, amazing in the woods and back country, but not a beginners animal.
8. Is a little more than 1/2 an acre a good amount for one horse?
Depends on the horse and how often / where you are riding it. I've kept 2 to 3 horses on an acre, you just have to irrigate or feed more hay.
Horses are super expensive, like Peaches Lee said, a good option would be to find a local trainer and take lessons. Even after you buy the horse, you have the farrier out every 6 to 8 weeks for a trim or shoes, feed, supplements if your horse needs them, grooming supplies, tack, blankets, fly spray, fly masks. The cheapest part is typically buying the horse.
Don't be discouraged by our responses, just be sure you are making the right decision for you and your situation!