I suggest you to start with the books "Molecular Biology of the Cell" by Bruce Alberts and "Molecular cloning: A laboratory manual" by Tom Maniatis. The first is an easy read which will help you to gain overall understanding of molecular biological processes and the second will provide a detailed knowledge regarding lab techniques used in this field.

Focus on your school lecture and read the recommended books/literature.

High ambitions are good but for that the foundations must be well laid.

You need to be more specific than that. People can spend a decade doing actual research, and can still barely be considered an expert on the single specific topic they are working on. Having the goal of "fully understand[ing] modern molecular biology" is not really doable with just a few online sources and some recreational reading time. It is an incredibly vast field where even those who have spent decades studying one sub-field will not fully understand the molecular biology of another sub-field.

If you are a med student then you should already have a broad idea of how the body works and what field you are most interested in (oncology, etc). Med students tend to lean towards clinical type studies and the science that drives those studies. I would suggest looking up a current health issue that you are interested in, looking up current clinical trials or past clinical trials to see what is or has been done. From there you can identify some supporting papers the trials are based on if they are available to the public, and then get an idea of how those field specific researchers are targeting the problem. In the materials and methods you will likely find overlapping or similar techniques, which should give you and idea as to what techniques are important for the field. Start googling from there to understand techniques and terms that don't make sense.

Doing this reverse method is a bit more efficient than trying to basically learn everything. If you are already in med school, you should have already attended classes that should have given a basic molecular biology knowledge. That combined with google and the plan I suggested should help you break into the field you are interested in.

"makes me comfortable with putting a hypothesis, a theory or possible treatment and testing this with the help of a specialized research team and as such"

You have a very long road ahead of you if this is your goal. Speak to an expert at school to make sure you are on the right path. You will likely need a little more than just reading online. They can point you to possible MD/PhD, internship programs, research programs, mentors who are running clinical research trials, etc.