Not cleaning the gravel in a non planted tank is not a good idea as it will create more problems in the long run and all types of bacteria will grow, good and harmful. Rooted plants naturally oxygenate the gravel and the mulm buldup acts as nutritients but you really need to have a lot of plants, not a few here and there to go the route of not siphoning. They need to be growing too, not dying so for that it takes a bit of time.
The problem you need to ask yourself is why is the gravel so dirty in a 70 litre tank with just 3 corys, causing ammonia to be released in the water column and staying there not getting filtered on time, which in turn causes brown algae(diatoms). I know you mentioned your filter is rated 320 L/H only, also that it doesn't pick up larger floating parts and from the video you posted on another thread the flow was to bare minimum, I would suggest you start from upgrading the filter which will help cope with any ammonia faster than the brown algae, and also would provide enough flow for waste not to settle in the gravel but picked up by the filter as it should. With 3 corys only you should have nothing to siphon in the gravel if you had good filtration.
Regardless of that, the tank is new and should eventually balance out with the diatoms disappearing completely. I've had it in all my tanks and I have done nothing to remove it. It just disappears but bad filtration and flow can cause it or cause different even nastier types of algae.
As for the cloudy water, it can be caused again by a substrate that has lots of waste, very low on oxygen and provides a lovely place for a heterotrophic facultative type of bacteria which is harmless and in anaerobic conditions converts organic waste to other stuff, but when in abundance, it will eventually make its way into the water column either by disturbing the gravel or even without, and then instead of eating organics, it starts taking up oxygen and starts multiplying rapidly,taking all available surfaces inside a tank like decorations, filter, etc... and can outcompete the filter bacteria in worse scenarios cause eventual ammonia spikes.
You best bet is good filtration and flow for a start. Plants will definately be a benefit regardless.