[Mechanic ideas] - Chain/Materialize/Beam

I like some of these ideas, and not others. With some tweaking, I think you've got something here, particularly with materialize. 

Chain is super confusing. So you get the effects of both spells (the countered one and the chain spell)? If not, this is terrible. If so, it's still wildly confusing (and creates a lot of rules issues). Which spell is chained, the one you cast with the "chain" keyword, or the countered spell that's chained to it. Which spell is exiled? The countered one, the second one, or both? If you aren't playing against blue, this is just a ridiculously complicated mini game you are playing by yourself in order to marginally boost your spells and possibly combo off, depending on what synergies exist for the mechanic. If you are playing against blue, you have the potential to lose two spells against a single counter, which is going to feel awful (even more than usual...). Furthermore, is it possible to chain 3 or more spells together, because it looks like it is. 

Materialize, as I said, has the most potential in my opinion. Spells that can become creatures are cool and flavorful, and the keyword choice is perfect to represent that. I think the wording and templating can be improved, however. I think that based on the standard format for alternate costs these days, it should be: Materialize <number> - <cost> (You may cast this spell for its materialize cost. If you do, it enters the battlefield as a number/number creature and remove the words in square brackets.) I'm not sure that you need the bit about it having other card types. I can't think of any situation where it would matter that you have an "instant creature" card on the battlefield or whatever. 

Beam is a bit odd. It's very similar to certain other mechanics, in particular multikicker. In fact, I think you should word it in almost the same way. For example, Beam <cost> (You may discard any number of cards as you cast this spell. For each card discarded this way, copy this spell. You may choose new targets for the copies.). It's hard to predict exactly what this mechanic would be like without trying it out, but my gut instinct is that it would be every bit as broken as storm and create as many, or perhaps even more, feel-bad moments. If you make the cost too low, a player could just drop their whole hand and pump the crap out of one creature, for example. Even the weakest spell effects would become overwhelmingly powerful if you can copy them 5 or 6 times. If you make the cost too high, the mechanic could become unusable and wouldn't support whatever synergies and archetypes you might have built into the set. You are already paying a pretty steep price in having to discard cards for the copies, but I would lean towards the latter option to prevent runaway victories and abuse. Another issue is that if you were to drop a bunch of cards in an attempt to make a big beam play, your opponent could counter and you'd lose a handful of cards instead of just one. Essentially, a single counterspell, if timed correctly, could be the end of the game. 

I hope that was constructive and not overly negative. Just trying to give you some feedback and maximize the potential of what you've got here.