Could I play in blitz tournaments only and get FIDE norms, hence I can get FIDÉ titles such as FM, IM, and GM?
FIDE describe the rules for titles including in norms in the document FIDE Title Regulations effective from 1 January 2022.
The first thing to note is that the FM title only requires reaching a certain rating. No norms are required for the FM and WFM titles:
1.3 Titles may be gained by achieving a published or interim rating at some time (see 1.53a). For ratings achieved after 1st July 2017, the player must at that time have played at least 30 rated games:
1.3.1 FIDE Master ≥2300
1.3.2 Candidate Master ≥2200
1.3.3 Women FIDE Master ≥2100
1.3.4 Women Candidate Master ≥2000
Regarding the rates of play for all titles it says:
1.1.2 There must be no more than twelve hours play in one day. This is calculated based on games that last 60 moves, although games played using increments may last longer.
1.1.3 No more than 2 rounds shall be played on any one day.
Each player must have at least two hours in which to complete all the moves, assuming the game lasts 60 moves.
In the application for the GM or WGM title based on norms, at least one norm shall be achieved in a tournament with only one round per day for a minimum of 3 days.
So, no each player must have 2 hours, not 5 minutes, for all the moves assuming the game lasts 60 moves. That is standard time control not blitz.
No you cannot. FIDE titles are only awarded for classical chess.