It is normal for the ammonia to waver a little in a brand new tank, even one cycled with biospira. It'll take a couple of weeks to settle down completely. However, during this time you should only feed sparingly - once a day, as much as they can eat within 2 minutes and no food left floating afterwards - is best.
As a rule of thumb, goldfish can tolerate ammonia levels up to 2 or 3 - although it certainly isn't good for them - depending on the tank pH and the breed of goldfish; some are hardier than others. Above this level however is when they begin to get burned and suffer badly. A nitrite level of above 2 is similarly toxic. Nitrates are
far less toxic however and it is normal for these to rise over time (hence doing partial weekly water changes). Just try to keep them under 20 ppm.
Hope this helps.

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I can't bear to see my fishes begging for food and I enjoy feeding them..
Water-quality is not the only problem which arises from over-feeding by the way; digestive problems and obesity can also be highly dangerous to fish over time. Many fish nowadays die from fatty liver disease, whcih is caused by overfeeding or feeding incorrect foods, so don't be too tempted to stuff your fish! Remember that in the wild fish eat only very tiny amounts which they have to search for continually through the day - they certainly don't have large regular meals supplemented by snacks delivered straight to them. Your fish will keep begging for food even when they are not actually hungry because this constant browsing instinct is very strong, but that does not mean you should keep feeding them.