Third octave D is not fingered the same as middle or low D. Although the right pitch will come out if fingered like middle D, it will be flat. Above is the correct fingering.
Saxophone players often use their F# fingering while on flute as it creates the same pitch but with worse intonation and tone. See above for example correct and incorrect fingerings for low and middle F#.
Third octave Ab is similar to high D in that the correct pitch will come out if you finger it like middle Ab, but the fingering above is superior.
As we learned in our first three notes on the head joint, blowing across the tone hole will make higher notes easier, and blowing more into the tone hole will help produce lower tones. Generally, this is good practice for playing the higher and lower register on the flute. However, in the extreme registers you may need to do the opposite. Notice the variety in air stream directions you have with the flute. Using your sound concept you have in your head, experiment with different air directions and air stream sizes to find the best tone and most consistent response.
Sometimes using the right hand pinky keys is awkward and can lead to poor seals. If a single key is slightly open, the low notes will not speak.
Flutes are designed to have their head pulled out slightly. Check your intonation on low and middle A and D. You may be pushed in too far.
If you have to pull out more than a half inch, you may have an embouchure issue. Try covering more of the tone hole with your lower lip.
If you are still sharp, you may have an air stream direction issue. Try rolling the flute in and blowing more directly into the tone hole.
Flutes are designed to have their head pulled out slightly. Check your intonation on low and middle A and D. You may be pulled out too far.
If you are pushed in all the way and still flat, you probably have an embouchure issue. Try covering less of the tone hole with your lower lip.
If you are still flat, try rolling out and blowing more across the tone hole.
Either your aperture is too large or you are using too much air to play. If you are breathing every couple of beats, you will over oxygenate your blood and get light-headed.
The flute is not designed to be played loudly and easily in the low register. Practice your harmonic exercises starting on your lowest note. Experiment with larger aperture and an air stream that is aimed down. Use a decibel meter app to track your progress and to see what gives you best results. Click here for an example decibel meter app.
The flute is naturally louder in the upper register and it can be difficult to control the volume and pitch. Make sure your air speed isn't too fast. Using harmonic exercises, practice changing notes with just your tongue position and air stream direction, and size. Experiment with a decibel meter app and tuner to find what works best. Alternate fingerings can also be valuable depending on the context.
Double and triple tonguing incorporate the back of your tongue to allow the playing of fast passages without slurring. Instead of just "toh, toh, toh" you would articulate like "to-go, to-go, to-go." Practice with and without the flute. Try just airing it, then add notes. Practice just the "go" articulation as slow as needed to get a clear articulation. Then add the front of your tongue and work from there. Use a metronome and a recording device to ensure evenness in sound and to track your progress.