It is hard to ascribe any one weapon as the mother of the tank, though many prior inventions have possessed similarity in aspect to tanks, such as the Hussite war wagon, the Roman Carroballista, or even, somewhat more metaphorically, the medieval knight. Tanks combine the ideas of protection, firepower and mobility in one neat package, a feat seldom achievable prior to the invention of the combustion engine as any sufficiently heavily armed or armoured weapon would have had limited mobility at best. It was the ability to combine mechanical locomotion with the striking power of modern weaponry and armour that offered the tank a unique place as a weapon on the battlefield.

The tanks seem to represent the cavalry in their aim but matching with the power of the artillery. Is it correct to say that?

The conditions and aims that gave rise to the tank were more of a result of the unique set of prevailing conditions brought about by the First World War. The tank was a mechanical solution to a serious operational problem; that the trench stalemate was considered (though not actually) impossible to break by normal means. Whilst the Central Powers resorted to infiltration and other unique methods to break the deadlock, the western powers of the Entente looked instead to a mechanical solution, designed to break through barbed wire, cross trenches, and thus open the battlefield back up to mobile warfare. The tank's early conception was thus more akin to a siege weapon than a cavalry arm, aimed to break into the enemy's 'fortress' of trenches and allow the traditional arms to do the rest.

Of course, this is not to say that the tank stayed that way, and it was the influence of early tank theorists such as J.F.C. Fuller and J.B. Estienne that saw more ambitious roles developed for the tank, although the two did diverge heavily. Fuller foresaw a mobile future for the tank, one in which he concluded that the tank would eventually usurp the cavalry's role on the battlefield and prove a decisive weapon of mobility. Estienne, a French artilleryman, saw the tank as a key tool to support the infantry, offering firepower and protection in the attack. Both of these ideas would remain highly influential for many years to come, and in combination could to some extent be considered to have created the doctrine of the 'universal tank', or the MBT as it is known today.

What is the importance of Napoleon for the invention of tanks? since cavalry in its time was losing space for infantry with muskets and the mobile artillery already showed its potential in the field of battle.

Although there will inevitably be other explanations, there are perhaps two that seem more pertinent. First, the Napoleonic era is oft regarded as creating some of the preconditions for 'total war'. The introduction of levee en masse, setting the stage for conscript armies, and the increasing industrialisation of war that would occur in the next century, helped create the necessary preconditions for a war such as the Great War to be fought, and hence the need to create the tank in the first place.

Also linked to this however, was the decline of cavalry as the arm of decision on the battlefield. Although they had been somewhat declining to begin with, over the course of the 19th century cavalry forces increasingly became relegated to roles of reconnaissance, flank support, pursuit and such, placing them in a more subordinate role than before, and whilst there were numerous reinvigorations of cavalry forces, enumerated in books such as Stephen Badsey's Doctrine and Reform in the British Cavalry, a niche was slowly created that armoured forces, beginning with armoured cars, but soon extending to tanks, could fill and eventually take over during the interwar and Second World War.

As for article recommendations, perhaps the best article on the origins of tank warfare that I have read is David Fletcher's 'The Origins of Armour', in Harris and Toase's edited book, Armoured Warfare, which I would recommend in its entirety.

I hope this answer suffices.