The side of Earth closest to the moon feels its pull the strongest, while the side farthest from the moon feels its gravity less.
Uhm, no.
The moon’s attraction is responsible for the larger tidal rise (bulge), while the sun’s attraction is responsible for the smaller high tide.
When the two bodies are in opposition, we have our lowest tides, when they are both on the same side of the planet (in conjunction) is when the highest tides occur. A “super” moon occurring while the sun and moon are in conjunction is what creates the highest tides, and is also why there are only 2 tides during that short period.