Welcome to Azeroth!
I can safely say that you are not “fairly new”
- you will be entirely new for a year, year-and-a-half. World of Warcraft is a BIG game. 
Despite that, you presented clear information, which is better than 90% of beginner questions, so 
Look in your bags. Type B or click the Backpack button toward the bottom right of your screen to open your bags.
In your bag, you should have an item labelled “Reins of the Scarlet Pterrordax”. Right-click that. It will disappear, and the mount Scarlet Pterrordax will appear in your Mounts list.
Now Mount it and ride. The Space bar makes you go up.
Incidentally, I just looked at your armoury https://worldofwarcraft.blizzard.com/en-gb/character/eu/turalyon/grompazz/ and it seems to me that you haven’t been putting on the new better armour and weapons you should have been getting as you quested.
While you are in your bags, try right-clicking any equipment better than you have. This will put it on, and make you stronger.
Gear Quality is shown by colour. From worst to best:
Grey = Poor (lowest)
White = Common
Green = Uncommon (Better. You should be wearing mostly Greens at 30)
Blue = Rare
Purple = Epic
Apart from Quality, each piece will have an Item Level. In general, the higher the Item Level, or the more Strength it has (Warrior wants Strength!) the better it is.
If youare having difficulties, I will be happy to have one of my Horde characters meet you to help with whatever I can.
Meantime, let me suggest the site Wowhead.com if you need to look anything up
OR you can look up any quests, itens and so on on YouTube.
For a beginner, I recommend this video:
it is MASSIVELY long, but broken up into 30-60 second chapters about different aspects of the game.
It is also out of date in that it was made just before Chromie Time was introduced, so it dosn’t cover that.
But it is very well made, and may make you aware of aspects you wouldn’t even think to ask about otherwise. You can then simply search YouTube to get more detail on anything you want to learn more about.
I find that searching YouTube is often the most practical way to find out about pretty much anything in the game, but you do have to be careful about getting the CURRENT information. Blizzard update classes and systems every expansion, and in a smaller way every patch. On the other hand, there are quests in the game that haven’t changed since 2008. So, look carefully at the video’s date and be conscious that some things have changed, and others haven’t.
If you want to know about the story of Warcraft, which spans tens of thousands of years, the previous games, and novels, you can look at Wowpedia https://wowpedia.fandom.com/wiki/Wowpedia or channel Nobbel87 on YouTube.