Do we need a lifting system as the architect suggests?

Make a sketch showing what is at which height and where the hillside location and street location can be identified. This is a considerable mess.

Your water drainage or sewer must be above the inspection chamber. Then everything is fine.

The toilet is lower than the sewer, but higher than the connections to the sewer, as I said, hillside location

If I understand you correctly, then your wastewater would first have to flow uphill to later reach the lower sewer connection. That only works with a "pump" for the first few meters, otherwise everything will flow back into the lower toilet.

No, just down.

My floor slab is at 332.5 meters above sea level. The surveyor's measurement points are also included. The road passes by on the right.

Bzp 334 is stated there. That means the channel is higher than the base plate and you naturally need a lifting system. What is unclear now? :)