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You can change the number of bits in the irsend.sendNEC(0xF0123,20) for example. Its under your own control. Try it out for yourself. remember you don't really need to send the F0 over the serial if it is always fixed. You will be sending a multiple of 8 bits every time over serial/RF.
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The 25° is the half angle so you get double. (+/- 25° =50°). Angle for IR emitters is usually quoted as the angle of half-intensity. You can get reduced power at a wider angles as per datasheet, paticularly at short range. On this IR LED it looks like up to a total of 60 degrees max.
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You should be able to get higher BAUD rates, particularly if you are only sending and not receiving. Worth testing. Try 200,000bps and 230,400 bps.
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Yes, you will need 3 receivers if you also need direction of travel.
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Re encoders/decoders ....probably best to stay within the comfort zone with that scale of project, intitially. There is always RevB !