I did a play test on a map with 5 people I have never played with before on a map I forged. I took two rooms an changed all the blocks to have a color. In those two rooms the lag is bad. I'm wondering if the block coloring would cause this?
Most likely not. Coloring forge pieces only changes the color of the glow, something that is already present on the piece anyway. In theory making a "rainbow" of colors all in one area for a bunch of different pieces could add to the memory use or something, but I doubt it would have a noticeable impact on framerates. This is all opinion and I have no actual testing knowledge of this. If you're absolutely worried about it you could try it and see if you notice any difference. If coloring a room all one color were to lag you noticeably, coloring a room 8 different colors would probably be worse. Good luck.
I've never heard of that causing frame rate issues. You might try the "avoiding frame rate problems" thread and see if any suggestions there fix it. I color pieces on basically all my maps and it's never noticeably changed the FR for me.
Well, the idea would be that loading the multiple colored textures would increase the running memory usage. I don't think that's at all how it's done anymore, though; I'm pretty sure the color is added through an RGB shift to the texture determined by a hex value ("Object Color") on the object. There aren't any more textures in memory when displaying different colors, just a few RGB equations that the XBox's GPU can do tens of millions of time while you add two and two. Kinda the same way that it doesn't matter what emblem/armor/color sets your Spartan is wearing. They're all loaded in memory, you're just choosing which part to render and what color it is. In theory, if there are enough objects being displayed as different colors this could choke your XBox, but your XBox would probably choke on the amount of objects it was rendering in this case anyway.