Have read your Betta saga ... the fish in temp fluctuations stress
easily. When they stress they lose their disease resistance. Written
info - on line if necessary recommends the calming restorative aids such
as Melaleuca (which is actually sold as Betta Care at $2.99 a small
bottle & Melaflor or some such in prices from $6.74 a large bottle at
Walmart to $9 at smaller pet stores.)
The product actually is derived from tea trees & is commended for many
fish especially Bettas.

The other alert .. and the aquamaniac poster has it as wellas others is
for 'flexibacter columnaris' ... a bacterium which thrives on fish
stress especially when fueld by food spoils and igher temperatures.

I lost two this past weekend .. includig a case of cottony fungus -
which was probably flexbacter. In my case, the temperature had been
gradually raised to 80F for a spawning. Also two 'housekeeping' fish in
the same tank had been fed another food which the betta occasionally ate
but regurgitated. Itwas the regurgitated food on the bottom of a
filtered warmer tank which provide a growth medium .. and perhaps the
stress of a newly introduced female.

The flexbacter treatment is referenced several places on line .. and
includes tetracycline. Also lowering the temperature --and watch the
fish stress-- slws the bacterium's growth.
A costly discovery but a permanent lesson - fortunately my bettas have
been replaced and the tank is ok.

As to filtering .. as with any 'clean' tank some debris may reach the
bottom ... yes your catfish or scavengers may consume it .. and yes your
mechanical filter will eventually collect it ..and no you won't see any
cloudyness as with overfeeding bacterial blooms ... but it will be the
growth medum the flexbacter needs if your temperature is up (it slows or
stalls below 76F ) and its signs are that fungus look, fin rot etc. SO
if a sponge filter or uergravel filter is in use and this occurs .
either assiduous syphon cleaning every few hours or eliminating the
food which causes it.

Good luck


Hope this helps.