From my experience speaking with kenyans, yes. The terms might be used differently other places, and sheng is notoriously flexible when it comes to grammar. So take it with a grain of salt, but you would not go wrong in assuming "Milk tea" rather than "tea with milk". It's also a pragmatic question, as the precise limits are not clear. How much milk is needed before tea with milk turns into milk tea?
And it's delicious. You should try it!
If you're translating directly, yeah - but there a lot of common phrases with qualifiers (often participles, but not in this case) like this that work in a similar way. I always thought of it as like "tea of the 'milk' variety". The only other example I can recall off the top of my head is "ndizi za kukanga", which is, like, cooked bananas.
There are a few different types of milk tea. In the USA, the kind we are familiar with is bubble tea. However, I read in Somalia they serve a slightly different variation called Shahi Haleeb or Haleeb shai (and by other names). The main difference is that bubble tea is cold with edible boba pearls while haleeb shai is hot and lacks these pearls. Somali is a recognized official language in Kenya, one of the countries where Swahili is prominently spoken. It wouldn't be a surprise to me if they are also familiar with this tea in parts of Kenya touching Somalia.
Probably not. At least in Kenya and Uganda they have this kind of tea that is made with more milk than water, so the translation "milk tea" is actually very precise. The way i learned to make it you just bring the finely ground tea to a boil in very little water (about half an inch deep), then you add quite a lot of milk. Usually you also add a lot of sugar.
White tea or Milk tea works just fine in Kenya.
It can be prepared by bringing to boil a mixture of water, milk, tea leaves and sugar. It can also be prepared by bringing milk to boil, and when serving the milk in a tea cup, immersing (or just dropping) a tea bag in the cup.
I wish to encourage (politely stressing) people to learn, to be open to other's experiences, your own experience of where you lived in a country of 49 million people with 42 tribes , how you spoke, the words you did not 'ever' use are not the important thing, you are here to learn something you do not know, something that might not know. Not everything needs to be equated or transferable to English. Just learn.