Hi Xavier and welcome to the forums!
You have certainly come to the right place as you will find all you need to know on budgie care here.
Since you are relatively new to budgies, the information on the several articles and sticky threads will be extremely useful and of benefit to you and your budgies.
It's still possible to connect with a pet bird, earn their trust and form a bond without using verbal communication. As you proceed with training and your budgies are more trusting of you, you can even use sign language by incorporating some simple signs as commands.
While it's true that it can be more difficult to tame two budgies who are already bonded with each other, by being consistent in the training sessions, you can at the very least make your budgies finger tamed.
The clicker training method might prove to be a very good option: https://talkbudgies.com/taming-bondin...-training.html
At first, it's important for them to get used to your presence and for them to realize you are not a threat and this can be done by sitting close to their cage and observing them while keeping a positive frame of mind.
By reading their body language, you will be able to tell when you can take the next step in the actual training by slowly introducing your hand and offering them a tasty treat to eat.
For more information on this subject, be sure to check the stickies on the Taming and Bonding section's main page: Taming and Bonding - Talk Budgies Forums
Regarding your budgie's diet, it's best that they are offered a variety of foods:
For all the detailed information check this section: Diet and Nutrition - Talk Budgies Forums
Best of luck with everything!