Well, since nobody is talking to you, I'll chat even though I'm just a newbie basically... My hopefully common sense thought is that you should take the taps off and inspect them for cracks and then think about whether and positioning or behaviours on your part might have contributed to the cracking. Certainly sounds like you might need new taps and o-rings at the least and you'll need to inspect other parts too. O-rings usually need regular vasaline lube treatment to prevent drying and cracking and this could be part of your problem. I also suggest you tell the forum your model in case that helps someone to give you more detailed help.
Another question is whether you are matching up the right hose size to the taps. There can be different recommendations by different makers of course.
As far as how long fish can go the experts will have to advise. My one thought there is that the most essential aspect of the filter is the biological function and of course there you want to achieve zero ammonia and zero nitrite. So without a filter and if you are not going to buy another and somehow cycle it and use it as your spare, you should go back to basics and do frequent ammonia and nitrite tests and use water changes to manually do what the filter should do. The reason I would expect it would be hard to give you an accurate number of days you can go would be that every tank is different with a different fish load and a different tank history!
Regards,
~~waterdrop~~
