This is something I bang on about all the time - but also from a safety point of view, tyres are a very complex and important component on a car (way ahead of the engine in priority, but most components and systems are too). Tyres effect the braking, steering, suspension, handling, road holding and comfort and noise of the car.
Unless things have changed with different materials used this is a NO, NO! You should have been told to take it easy on the tyres for the first 100 miles or so (200 if wet) as tyres are can be 'greasy' (forget the correct word) from new plus you need to get used to the new tyre's characteristics. They also (used to) tell you to check the wheel nuts (horrible bolts on these) for tightness after about 30 miles.
Remapping reduces the margins put in by the manufacturer for the very varied use the car will get though all sorts of conditions so can be more wearing on the car, more care, attention, maintenance, servicing, parts, consumables and their quality may be required, insurance to be notified. Similarly to a car being driven hard all the time. I'm not against spirited driving, I encourage it where suitable, and certainly occasional Italian tune-ups may be needed even more by modern cars.
Just because there are no error codes showing doesn't mean information isn't showing deeper, a proper VW scan with live data on a run might point to things to investigate.
I've never driven an S3 only passenger'd in (a new) one about 5 years ago but having driven my wife's Fabia I'd say there must be something wrong as I don't feel the Fabia SE 1.2 TSI chassis is particularly 'sporty' and should easily be shown up by a S3.
I get the feeling you're probably a few decades or more younger than me so have different experience and attitudes so may not agree with or like my old fart advice but it's here anyway.
Do not rely on the car's electronics, use your own computer first, what's between your ears, you can prevent problems and issues on the car before it needs to warn you about them or tell you when it's already too late. With driving you can get the car into more trouble sometimes than the car's computers can fully prevent or rescue you from.
Don't worry about how high you can get the speedo and rev counter needles or numbers it's all about how it feels not ego numbers, the better it feels at lower numbers the better for everyone and everything. Unless you're in adverse conditions, in which case you'd be going slower, the 4WD, only helps you go too fast for any good road feel, you could get better feel from lower speeds without it. The speed limit on single-carriageways is 60 mph, where's that on the S3 dial (or even Fabia).
James Hunt a F1 Champion used to drive an old Austin A35 slow very low powered van (Wallace & Gromit van) for a few reasons but got a lot of fun out of driving it in a very spirited way, it's not all about what you've got but how you use it.
Now here a bit most men don't like, and this from a man who isn't a good driver - one of the very best tuning aids for any car is driver training, and you can transfer it to each car without cost or hassle and may decrease rather than increase insurance premiums. Most men will think they're already good drivers and some will be (not me) but can improve with this investment.
Wheelspin is generally the driver's loss of control over his vehicle, not driving to the conditions or anticipating road conditions, if you've got unexpected wheelspin because you're driving too fast or road conditions you'd slow down - if you weren't driving too fast and it's a fault of the vehicle or its computer systems then it really needs sorting.
I bet that's upset a few (many Fabia?) readers.