안녕하세요!

1) There's 2 different ways I can explain this :

all proteins by definition, will have a tertiary structure, because all proteins must have at least one polypeptide strand.

not all proteins will have a quaternary structure, because not all proteins will have more than one polypeptide strand.

so in terms of which structure will be most important for "ALL" proteins, tertiary structure is the most important.

another way I can explain why the tertiary structure is the most important is,

often the tertiary structure determines the overall shape of a polypeptide strand, including the shape of the active site.

When thinking about various enzymes, where the function of the enzyme is dependent on the shape of the active site,

the tertiary structure determines the overall shape, including the shape of the active site,

therefore, the tertiary structure is the most important in determining the function of the protein.

2) quaternary structure is simply defined as interactions between separate polypeptide strands,

therefore these interactions can take all kinds of forms, including, R group interactions, hydrogen bonds, ionic bonds, etc

3) yes, the secondary structure of proteins is defined as hydrogen bond interactions between amine groups & carboxyl groups of different amino acids,

usually forming alpha helix or beta sheet motifs.

there are no other interactions that are referred to as secondary structure of proteins.

In fact, these secondary structures are so specific, that every turn of an alpha helix motif is calculated as occuring in 3.6 amino acids per turn.

4) Tertiary structures are more complex, and are often determined by what is most favorable from an energy perspective.

Long chains of polypeptides can be coiled or shaped so that R group interactions form bonds that are stable and hold the entire polypeptide in place.

But, tertiary structures can also be manipulated by other factors as well, 

for example, certain chaperone proteins help ensure that proteins are folded a certain way, with specific R group interactions that may not naturally occur when left alone.

so to answer your question, 

yes, tertiary structures are formed due to R groups, but how the R groups interact can be modified in different ways.

The study of how proteins fold and function is called proteomics and is an extremely hot topic in the field of biology.

Exactly how a polypeptide strand folds into specific 3D shapes has been a puzzle many scientists have struggled with.

International competitions would be held with teams from all around the world competing to have the most accurate predictions of how a polypeptide will fold.

In the past few years, teams armed with artifical intelligence have blown the other human only teams out of the water, with ridiculously accurate predictions

With the advancment of AI, protein modeling accuracy is expected to increase astronomically in the next few decades,

which may open up possibilities for humans to design proteins from scratch to perform a specific functions. Really amazing stuff!

https://deepmind.google/technologies/alphafold/

Really good questions! I can tell just from your questions how hard you are studying.

Hope these answers help and keep up the good work! :D