Yes and no.
The ‘no’ first: Airtable is not a spreadsheet, which functions in a 2D space. Instead, it is an RDBMS with a spreadsheet-like (or, rather, spreadsheet-ish) UI. In Airtable, each row represents a separate database record; each column presents a field present in each of the records. Each tab represents a different table in the database. Individual rows in one table can be linked to individual rows in another table (that is, such links span tabs), and based on such links, fields from one linked record can be accessed in other linked records.
However, keep in mind there must be an explicit link from the record (row) in question to the record (row) referenced: There is no such thing as, um, reference via reference: The physical relationship among columns and rows is only a function of the current display configuration; there is no presumed relationship based on physical placement. In other words, you can’t reference a field two columns to the right and three rows above the current field, because such a thing doesn’t exist. Which record is three above the current one depends on how the view is sorted and filtered; which column is two to the right depends on what orders your columns are arranged.
Accordingly, Airtable formulas operate only within the context of a single record, and they reference other fields in that record by name, not absolute or relative position. While there are ways of performing cross-record calculations, they are of necessity rather baroque, and they all work by finding ways of using a web of linked records to make field values from multiple records accessible within a single record.
In brief, then, your first example functionality — entering a row:column cell address and having the value of the referenced cell appear in the current cell — is not possible.
However, your other example — using fill handles to replicate field values quickly — is possible in Airtable; however, I suspect without the former functionality, it will be of less interest to you.
There are other significant differences between a spreadsheet like Excel and an RDBMS like Airtable — because, again, Airtable isn’t a spreadsheet. Probably the most significant one is that currently in Airtable a formula can only change the field containing that formula. In other words, you can write a formula in Field A that says, “If the value of Field B is 10, then make Field A equal 20,” but you can’t write a formula in Field A that says, “If the value of Field B is 10, then make Field C equal 20.” It’s a subtle but significant difference, and it can take a few cycles to wrap one’s head around how your programming style needs to change accordingly.