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I wonder where were the astronauts more comfortable spending the day, sleeping, dressing the space suits, etc: the LM or the Command Module? Considering, of course, that the Command Module would carry three crew members while the LM would carry only two of them. Which of these living spaces was more comfortable for a crew member ? Also wonder, was the Lunar Module accessible during the Earth to Moon traveling ? Or the hatch between the two modules was kept closed ?

The command module was more spacious and comfortable. Below the crew couches was an area called the "lower equipment bay", which was where, among other things, the personal hygiene equipment was; it afforded a small amount of privacy for bathroom duties. Crew could either sleep in their crew couch or in a sleeping bag attached underneath the couch in the lower equipment bay.

Here's a cutaway of the CM:

In contrast, the cabin of the LM was quite cramped. The two crew members could stand side by side, and there was some additional space behind them above the ascent engine cover. Sleeping was very awkward; on Apollo 11, Aldrin slept on the floor and Armstrong on the ascent engine cover for an uncomfortable 4-hour rest period; the later crews had hammocks mounted so:

According to Wikipedia, the habitable space per crew member was pretty similar, even a little in favor of the LM (6.2 m³ living space in the CM versus 4.5 m³ in the LM), but there seems to have been a significant psychological effect to being able to get out of sight of one's crewmates briefly in the lower bay.

Was the Lunar Module accessible during the Earth to Moon traveling ? Or the hatch between the two modules was kept closed ?

Normally, the hatch between the CM and LM was kept closed. The LM was powered down during the translunar leg of the mission, so it was uncomfortably cold; keeping the hatch shut also slightly reduced the risk of a micrometeroid strike depressurizing the spacecraft. The LM was normally opened briefly during translunar flight for a checkout/inspection, but the hatch was re-closed afterward.

After the explosion on Apollo 13 forced the crew to move to the LM, the hatch between the CM and LM was left open. The crew needed regular access to the storage lockers, hygiene facilities, and other conveniences of the CM, and they used it as a sleeping area, since the LM was really not suited for three crew members. Getting to sleep in the extremely cold CM required remaining very still in order to maintain a thin envelope of air warmed by body heat; with the CM's air circulation fans powered off, and no gravity to cause convection flow, the warm air would stay in place.