Space is indeed an element. Xuan Lao and Di Tian have also control over space but it is different with Space Attribute/Element Spirit Master. Spirit Master that have Space Element are naturally able to wield the power of space and use it to the best their abilities can when they awakened their Spirits. However Xuan Lao and Di Tian are able to use the power of Space because they can already sense it. You can also call it as Profound laws of Space in other Xianxia Novels. When one reaches Title Douluo (9-Rings), they can already start sensing the Laws/Ways of the world. They will then start to sense and understand the mysteries of the Space Element and as their cultivation increases, their understanding towards Space Element also increases. Only when one reaches Limit Douluo or the someone on the same level as Di Tian and Mu En(Dragon God Douluo in DD2) can they start using Teleportation. This is because they already have a very profound understanding towards Space and they can use it to this extent. Di Tian was even better at using Space because he use the Element of Space as the basis to his Second Spirit Core. On the other hand Space Attribute/Element Spirit Master have a natural affinity and ability to be able to use the power of Space. You can also compare it with Flying Type Spirit Masters. Flying Type Spirit Masters have the natural ability to fly but ordinary Spirit Masters need to reach Spirit Sage/Saint(7-Rings) to be able to fly. Space Attribute/Element Spirit Masters have the ability to Teleport and Control Space while ordinary Spirit Masters first have to reach Title Douluo(9-Rings) to be able to sense the Laws of of Space then if they have sufficient understanding towards Space, they can wield it to some extent or finally even Teleport.
Now towards Spirit Cores. Spirit Cores are established when one reaches Title Douluo(9-Rings) Level because their Spirit Force are already very dense and to condense it any more would make it solid (Spirit Force = Gaseous State - Liquid State - Solid State/Spirit Core) but a Solid Spirit Force cannot circulate within the body so they instead condense it to Spirit Core in order to once more advance in cultivation. The Element of the Spirit Core is based on the Element of the Spirit Masters. For Example, if a Spirit Master was Flame attribute then the Spirit Core they would condense would also be based on his/her Flame Element becoming a Flame Attribute/Element Spirit Core. Their strength and control over the respective Element would also increase. Normally a Titled Douluo(9-Rings) will only have one Spirit Core and they would only establish their second Spirit Core when they are trying to break through Limit Douluo(Rank 99). As most Spirit Masters only have a control towards a Single Element they based their Second Spirit Core on Space Element(You can't create two Spirit Cores that are both of the same Element because all your Abilities or Energy towards the Element you control are already fused with the Spirit Core that you first established) because they already have an understanding towards Space Element. Well other Titled Douluos with Two Elements can use their respective Elements as the basis for their Spirit Cores. Mu En's case was the same as this and based his Spirit Core on Lightning and Light Elements. On Di Tian's case, since he only had a single Element(Dark), he based his Second Spirit Core on Space due to the fact that he already has a very high understanding towards because of his long years of cultivation. So after establishing his Space Spirit Core, Di Tian's abilities towards Space greatly increased granting him the power of Teleportation and other Space Related Abilities. This is the difference between a Space Element Spirit Masters and cultivators like Di Tian. Even if a Titled Douluo(9-Rings) or a Limit Douluo(Rank 99) has a second Element and didn't use Space as their Second Spirit Core, they can still use the power of Space to some extent because they have an understanding about it.
Beast God Di Tian and the other 10 Great Ferocious Beast on the continent being not known in DD1 was never mentioned. Though my guess is that during DD1(20000 Years Ago), the Spirit Masters at that time still weren't advance enough to threaten the Spirit Beast and the Core of Star Dou Great Forest that the people knew(Da Ming and Er Ming's area) probably wasn't the deepest place in the forest because the Spirit Masters at that time didn't have the strength or power to go any deeper/further within. Though Spirit Hall and other major organizations at that time were quite powerful, the Spirit Beast still probably didn't think they were enough to threaten them so they didn't bother meeting up with them. On DD2, the number of Spirit Masters already increased and their strengths also increase compared to DD1 such that other people were able to absorb Spirit Rings surpassing their limit(6 -Black, 3 - Red) and the theories Grand Master(Yu Xiaogang) left on Shrek Academy let many people know a better way to cultivate. The advancement of Spirit Masters probably made the 10 Great Ferocious Beast of the Continent felt threatened and they finally made contact with Humanity, letting their existence be known.
Hope it helps... Though there's still some stuff about Spirit Cores that I didn't say...