I will try to clear your confusions line by line.
Gaudiya Vaishnavas claim that they follow the supreme Godhead Krishna
They don't, They follow instructions of Krishna in Gita.
- Krishna indeed said chanting of names is a sacrifice and one must always think about him while doing one's duty.
Amongst chants know me to be the repetition of the Holy Name(BG 10.25)
Arjuna, you should always think of Me in the form of Kṛṣṇa and at the
same time carry out your prescribed duty of fighting. With your
activities dedicated to Me and your mind and intelligence fixed on Me,
you will attain Me without doubt.(BG 8.7)
Always think of Me, become My devotee, worship Me and offer your
homage unto Me. Thus you will come to Me without fail. I promise you
this because you are My very dear friend.(BG 18.65)
- Krishna indeed preached non violence as Dharma and asked Arjuna to fight war in "Yoga"
Nonviolence; truthfulness; freedom from anger...these transcendental qualities, O son of Bharata, belong to godly men
endowed with divine nature.(BG 16.1–3)
Do thou fight for the sake of fighting, without considering happiness
or distress, loss or gain, victory or defeat – and by so doing you
shall never incur sin(BG 2.38)
Perform your duty equipoised, O Arjuna, abandoning all attachment to
success or failure. Such equanimity is called yoga.(BG 2.48)
The spirit soul bewildered by the influence of false ego thinks himself the doer of activities that are in actuality carried out by
the three modes of material nature.(BG 3.27)
Those who see action in inaction and inaction in action are truly wise amongst humans. Although performing all kinds of actions, they
are yogis and masters of all their actions.(BG 4.18)
- Foods are recomemnded based on Sattvika Rajasika and Tamasika elements. Ksatriyas indeed have Sattva and Rajo Gunas.
Persons in the mode of goodness prefer foods that promote the life
span, and increase virtue, strength, health, happiness, and
satisfaction. Such foods are juicy, succulent, nourishing, and
naturally tasteful. Foods that are too bitter, too sour, salty, very
hot, pungent, dry, and chiliful, are dear to persons in the mode of
passion. Such foods produce pain, grief, and disease. (BG 17.8-9)