After the single point in skills that require it, there is nothing you "need" to spend training points on.
That said, most people spend the majority on trade skills. As an INT caster, Research is available to you, plus all of the basic ones, but you have time to decide. That and it can get really pricey as you get up there, so it's not usually something you do in the early levels anyway (spend ALL your points, I mean).
As for Specialization, increased skill there lowers the mana cost of spells from that school. Those skills will increase just as the schools themselves increase (just cast spells from that school for a chance at an increase). The first one to 51, however, is the only one that can continue above 50. There is a quest in the Temple of Sol Ro that will reset your specs, but usually you just want to decide which one you want (not an expert on Necros, so someone else will have to chime in there) and just cast spells of that school until you hit 51 and then never worry about it.
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