3) Will 3.3v be able to run 16 ws2812b? I plan to not use much brightness or white, only reds and blue at low intensity.
I've done it (mostly using one or two 16-LED rings), but it really depends on the strip. You won't be able to do anywhere near full brightness. Some strips will not run at 3.3v, and you need higher voltages.
Usually in my scripts I set the maximum for the sum of the R, G, B levels to be 30. This gives a value of about 75 mA for 32 LEDs when powered at 5v. Perhaps 113 mA at 3.3v, which is under the 250 mA that the Teensy's can supply for 3.3v (remember, you have to include the Teensy itself in the power calculations). IRC, blue LEDs take the most power.
I would suggest incorporating something like a SN74LV1T126 into your design, and feed power from VIN instead of 3.3v to power the WS2812B LEDs. That way if you have to replace the LEDs or upgrade them, you won't run into the situation where the LEDs won't run on 3.3v power.
Even if you use the VIN pin, you won't be able to do more than about 6 LEDs at full power. IIRC, WS2812B's tend to be around 60mA at 5v power at full brightness. You can generally get about 500mA from the VIN pin (assuming the USB power source delivers somewhat more than 500mA). Figure maybe 75-100mA for running the Teensy. That gives to 400mA power you can use for the LEDs. At 60mA per element, that gives roughly 6 elements that can be run at full power.
I'm a software guy who hasn't designed a PCB, but I suspect you may need to think about things like ground planes and 3.3v to distribute the power.
But in general, unless you are doing stage productions in a dark room, you want the brightness to be way down. I've had people say even the 30 level is too bright if I'm close to them.
(note, in case it isn't obvious, these are all back of the envelope calculations, they might not be right in detail, but hopefully the spirit of them is correct). Over times the power draw for WS2812B leds has changed, and there are now at least two manufacturers of them. Also the amount of power that the Teensy draws can vary depending on the processor, battery saving usage, and cycle speed.
If you are able to get the full 5 volts and 2.1 amps available from some power supplies (attaching the power before the USB connection), by my back of the envelope calculations, you might be able to get 32 LEDs at full power.
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And in terms of push button switches, it may make sense to use 2 MCP23017's to handle all of the digital inputs, rather than attaching 20 push buttons to 20 pins. You would have to reserve pins 18/19 to run the I2C bus, and possibly put 2 2.2K pull-up resistors on it. It would allow you to add more digital push-buttons (or simple LEDs) in the future. In terms of microprocessor speeds, I2C is a fairly slow bus, but for human reaction speeds they aren't bad. Obviously as you get to more inputs, you have to start thinking about optimizing the read speed of that many switches. For example, there is an interrupt pin to say a switch changed, and you can read the switches in groups of 8 instead of doing individual reads for each switch.
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There are ways to reduce the number of analog input pins used as well, but I'm not as familiar with them.