The capital exerts more loyalty pressure compared to other cities, so take it into consideration. Conquering a very basic city right next to their cap, while at the same time so far from your lands, is asking for a city flip.
You build pressure with population (from your city and others around), amenities, monuments, some buildings and governors. Victor is a good choice to minimize loyalty problems in conquered cities, as he establishes in 3 turns and can be promoted to generate loyalty in surrounding cities. But Id say the safest way to hold is to plant a city with good growth tiles close to your desired target, chop some food if you want to boost it fast and start picking the closest cities. Regularly check the loyalty lens so that you can determine what you need to do next.
Also, Im not seeing any tile improvements in your starting cities, you need to tap into those resources (especially those amenities you havent improved and the pastures, considering you are playing as GK). You are missing out on critical resources (and eurekas and inspirations) which will boost your progress significantly.