The choice of stereo/2.1 speakers with SPDIF connection is pretty slim. Most speaker systems with digital connections tend to be surround. Are you looking for stereo and what you are looking to spend?
Stereo or 2.1 is going to be best way to go for up to £100. Any 5.1 speakers with SPDIF input for around £100 are not going to be worth having, assuming they even exist at that budget. I think the best thing to do, would be to buy a DAC (digital to analogue converter) with SPDIF input, possibly a FiiO D3, then to that you can add any speakers of choice, whether they be stereo or 2.1.
The choice is so small of stereo/2.1 speakers with SPDIF input built in, I can't really think of anything other than Behringer MS20 for £95. With a DAC, you can add whatever stereo/2.1 speakers you like, you are not limited to one or maybe two speaker choices, such as the MS20.
Any powered speakers will work. Hi-fi speakers won't unless you have an amplifier. Powered speakers have the amplifier built in.
Yes, although best to remove the link as it's a competitor. Powered and active are the same thing. It means the speakers have the amplifier built in, and plug into the mains to get the power they require. Such speakers will either have RCA/phono or 3.5mm connections. The FiiO D3 DAC has RCA/phono connectors, so if the speakers 3.5mm, a cable converter can be used.
Passive speakers which are more common in hi-fi setups require a separate amplifier to provide the power they need.
For 2.1 speakers using SPDIF, look at "Soundbars".
I can't vouch for the sound quality though, they will set you back several hundred pounds.
Optical and coaxial are different types of cable. Both are digital, but optical commonly known as a toslink cable, uses light pulses, whereas coaxial uses electrical signals and has a RCA/phono connector.
If you'd rather get a soundbar, then all you need is a standard toslink cable to connect from the Android device to the soundbar. You won't need a DAC as well, as the purpose of a DAC is to convert digital to analogue so any powered/active speakers can be used. The soundbar is a speaker and DAC in one, so you just connect the optical/toslink cable.
Some will have both optical and coaxial connections, whereas others make have one or the other. What make and model is the soundbar?
It has both, so as long your Android device has coaxial SPDIF, then the cable you've bought will be fine.