Pure chakra is chakra without any additions made to it.. so as i said before its the combination of the mind and body and it circulates through the chakra system and its essentially the life force of any ninja, it is what we use for ninjutsu, genjutsu and taijutsu and even the most basic ninja techniques.
Elemental chakra is chakra that a ninja has changed the properties of.. for example wind chakra doesnt become wind chakra unless the user can effectively grind his chakra together, creating and imagining it as a sharp blade and through this process pure chakra becomes wind chakra
Nature transformation takes place after the user has properly moulded and changed the properties of his chakra and effectively added it to his jutsu or weapon, it is an advanced form of chakra control and is one of two necessary techniques in order to create a tehcnique, its counter part being shape transformation.
There are 5 different nature transformation which i have previously already mentioned but for the purpose of the question i will mention them again, Fuuton, Suiton, Katon, Doton and raiton.. these 5 nature transformations are foundation of all elemental ninjutsu.
There are more advanced elemental transformation however all of which involve the basic elemental nature transformations as a base, aside from the five basic types of nature transformation, there is also a sixth type the Yin and yang, yin being the basis of imagination and spiritual energy used to perform yin release and yang being the basis of vitality and physical energy, used to perform yang release.
Together they are used to perform yin-yang release and is the basis for most non-elemental ninjutsu such as the shadow imitation technique
Handseals are used to perform ninjutsu, genjutsu and other secret arts other than taijutsu, the chakra necessary to perform a technique is manipulated through the use of handseals.
there are a different set of handseals for every technique.