Yes, you're writing a fantasy story. Yes, that means many of the normal "rules" of reality are suspended. It doesn't mean you can just write whatever you like and expect your readers to swallow it. The existence of dragons they'll probably accept. Moscow being the capital of France they probably won't.
The key to "selling" weird, fantasy stuff to your reader (like dragons and half-elves) is making the world at large believable. This means getting the simple things right. So on that note:
1. Factual Errors
There are things in the wide-world of fiction that are fantasy elements; things like dragons, unicorns, and women who find beards sexy. There are other things in the wide-world of fiction that are factual elements; things like the speed of an average horse, the boiling point of water, and the observation that iron rusts.
Clearly, these are not two distinct categories that can have a line neatly drawn between them. You may have created a world where one of the fantasy elements is that water boils at fifteen degrees (making a lake on a warm day hilarious). I could totally go with that. The important thing is that you are clear which category you're operating in. Readers will spot factual errors for what they are if you don't make it obvious that this is an intended fantasy element.
Example: A horse can't gallop all day. While horses are bred to cover many miles before exhausting, they do this most effectively at a trot. A fit horse can go maybe three miles at a gallop before tiring out, but over fifteen miles at a trot. If its a magical horse, then knock yourself out. But be clear that it is a magical horse.
Another one: There is no special place on the human head that you can hit to render someone unconscious without risking brain damage (and certainly waking up with the mother-of-all-headaches). If someone receives a blow to the head that leaves them unconscious for more than a few minutes, then they have what doctors call a Grade III Concussion.
So don't have your noble knight do it to his girlfriend, alright?
2. Straining the Limits of Plausibility
Even without making any distinct factual errors, it's still easy to strain the limits of what a reader will accept without incredulously rolling their eyes. The line between "heroic" and "god-like" is a fine one, and it's worth developing a sense for when you've crossed it.
-> In the real world, a talented individual who starts fencing at the age of ten isn't likely to reach international recognition before they're in their late teens or early twenties.
-> In a fantasy story, the humble (but mysteriously talented) farmboy who spends all his time training with a legendary warrior, might be capable of going toe-to-toe with the Dark Lord's lieutenant after a few years.
-> In a bad fantasy story, he can best his master after three months.
I think most people can probably think of a book they've read that includes an example of the above, but problems with unbelievable martial prowess are only scratching the surface. What lurks below the surface (like a waiting crocodile or a submerged corpse) is the following:
Protagonists with the stamina of the Duracell bunny and the resilience of granite; making tender love to their third wench of the night having broken both legs just two hours earlier. Who can forge a sword having only previously watched one being made, or tame lions because they had a mean cat when they were a boy.
Such characters have progressed beyond heroic, and are now simply unbelievable. And readers don't invest too much in unbelievable characters.
3. Inconsistent Technology
"But surely only science fiction writers have to worry about technology!"
If the people of your fantasy world have invented the hand-axe, then they have technology. And if they have technology, then you need to worry about keeping it consistent.
This doesn't mean you have to accurately represent a particular historical time and place in your alternate-world sword-and-sorcery yarn. (Although that's a good start if you're not sure.) It just means paying attention to the rough order that various technologies tend to be invented in.
A possible place to start: In your fantasy world, have black powder weapons (cannons, muskets, etc.) been invented yet? Well, cannons first reached Europe (having been used in China for ages) in the 1200s. So if they haven't appeared in your fantasy world yet, then that puts down a rough marker of the sort of technology level you're talking about.
For example, it would be highly surprising for a world without black powder to have hay bales in its fields, as the hay-baler wasn't invented until the 1850s (over six-hundred years after the appearance of cannons). That would be a civilisation that has invented heavy machinery, but has completely failed to discover that a rough mix of charcoal and saltpetre (a chemical easily extractable from human urine) will explode violently when lit.
4. Fantasy Stew-Pot
Like spices, fantasy elements are best used in moderation. The more weird stuff you introduce, the more stuff you have to "sell" to the reader. So piling in every single mythical creature, fictional race and mystical artefact that you have ever read, seen or madly dreamed up is not the best plan.
Readers will happily swallow your fantasy world occupied by elves and dwarfs. They will still probably be fine when you add dragons and unicorns. But throw in fairies, angels, demons, vampires, werewolves and Cthulhu, and now you've turned your delicious fantasy soup into an almighty mess.
And - as with spices - combination is just as important as quantity. Some fantasy elements have a certain "synergy". Vampires and werewolves; elves and dwarves; dragons and men-wearing-impractical-metal-outfits. These pairs go together like chedder cheese and Branston Pickle; effortlessly. Other match-ups take more work.
Example: Your fantasy world already contains vampires and werewolves. Classic as vanilla ice-cream, so no problems there. You add witch-doctors and zombies for a bit of chocolate sauce. We're still in the arena of pulp-horror monsters, so all is well. Then a leprechaun shows up, like a short, green sausage thrust into the middle of your sundae. It's not pleasant.
It's not that you can't do this, but you're going to need a lot more heavy selling to get your reader on board with it. You can drip-feed the new elements (e.g. only introducing two races in each book), or tinker with them until they represent something more in keeping with the rest of your world (e.g. swapping traditional vampires for blood-sucking tree-monsters, the better to fit in with your forested elfy world).
Alternatively, you can write a spoof, and thus throw all the above rules out of the window for the sake of good comedy. But that's a different kettle of fish entirely. (And fish doesn't go with ice-cream either.)
5. Narnia, by MC Escher
Of course, there is a way to completely dumb-found all those nit-picking readers who'll complain about every factual error and implausible event they find. And that's to make your fantasy world so incredibly, obtusely, barbarically weird that the reader has absolutely no idea what to expect.
You've set your story in a fantasy world where the fundamental laws of physics left on the same life-raft as logical human behaviour and basic economics, thus allowing your Merry-Ship-Fantastica to sail gaily away into a vortex of sheer lunacy.
Believe me, there's no faster way to make your readers jump ship as well. The further your world strays away from the real one, the less readers have to connect them to it. So - like it or not - you need to know things about this world before you can create your own.
And remember, Google knows all!