check the battery first including connectors are clean and well tightened
but it seems strange after a few attempts it starts, so you could possibly be looking at coil pack even, the sparks are at the top of the engine iirc under the black cover, with individual coils packs for each sparkplug
another cause could be a sticky starter motor, e.g the gear is NOT fully extending to engage with the flywheel (possible starter solonoid failure) but you can still hear it spinning
what you are showing at 2:50 is the injectors on the fuel rail, they are electronically activated solenoids and on all recent cars i have owned and worked on (peugeot 207 1.4 8v, alfa romeo mito cloverleaf,
seat ibiza with the same engine as yours, also 1.2 tsi engine, focus rs etc) you can hear them more, it has caused me understandable concern before but it is just how they work, if you hold the revs at approx 1000-1500 you may notice the noise increase in rate
thats what my thoughts are after listening and watching your video