What does the DBMS do exactly when i send it a SELECT query regarding the .frm files and database pages? (MySQL)
The .frm file contains nothing more than the schema.  It is looked at when opening the file, then info is kept in RAM.

ibdata1 or the .ibd file is the "tablespace" for the data.  It contains meta info about the data, indexes, etc.  In particular, it points to the root nodes for the indexes of the table.  (Note:  The data is stored based on the PRIMARY KEY, so the "data" acts very much like an "index".)

From the "root" node of a B+Tree, you can drill down to an individual row.

From an individual row, it is possible (when doing a range/index/table scan) to easily find the next/previous row in the B+Tree.

The BTrees are organized in 16KB "blocks", pointed to by a tuple that contains (approximately): tablespace number and block number.  Since a tablespace is a file, the block number is easily translated into a byte offset in that file.  The OS has an extra layer of looking up such a logical address to find a physical address.

Within the Block, there may be, say, 100 "records" that are either data rows or index rows or links down the BTree to other blocks ("nodes").  (The "100" is a Rule of Thumb; in reality, it could be as few as 1, to as many as several thousand.)

To find a particular row (other than the "next" or "previous") within a block, some form of search is done.  (I don't know whether this is a linear scan or a binary search.)

SELECT name from mytable where id&gt;1



Parse the command.
"Open" the table -- either cached (cf table_open_cache) or use .frm (or Data Dictionary in MySQL 8.0)
Figure out how to perform the query
Find index on id.  Let's say it is PRIMARY KEY(id)
Locate root of B+Tree for the PK
Drill down until locating the last (or, since a PK is unique, the only) row with id=1, then start at the 'next' record.
Scan forward, fetching name from each row until you hit the end of the table.