I've been told by a fellow foreigner who recently sorted out her own place that I should be wary of agencies quoting me much higher prices because I'm not Polish
That might have happened a few years back (although it never happened to me even a decade and a half ago), it doesn't happen now. The reason is that you see real properties advertised on the web (domiporta.pl and oferty.net are the best ones) and then you call about that particular offer. You've seen the price online and if they try to give you a higher one, just hang up.
most of the tap water in Warsaw comes from Vistula river as far as I know - would you drink it from the river?
Where were you expecting it to come from, the Nile? The water which comes out of Warsaw's taps is from the Vistula and has been thoroughly filtered.
do you believe they filter it out with Brita filtres?
I know for a fact that they use rather better filters than a Brita. It's filtered through sand (twice, different fineness, active charcoal (twice) and friendly biological agents. Then it gets a splash of chlorine and a dash of sulphur.
I really do have no idea why people are so down on Warsaw's water. The Warsaw water filters are currently short-listed for UNESCO world heritage status. No other municipal water filtration system has been listed there!
there are parts of Wroclaw that have their own wells and water is much better there
Pretty much everywhere in Warsaw has public springs. Mineral water for the people who don't want to pay for it and can recognise that using trucks to transport water is about as environmentally friendly as a bucket of napalm.