@Akire
Sign language translators are hearing or they couldn’t do their job. So they just translate the verbal English into BSL.
Not always true.
Some are deaf and translate from written English. And sometimes you can tell.
You occasionally get deaf relay interpreters to interpret from the interpreter's BSL to grass roots BSL.
OP
In BSL you 'chunk' information, the signs are in a different order to English words so if some one said in English, "I put a glass on the table" you would have to sign it as, "table, glass, put on" but you have to use the correct, 'table' and 'glass' because the English word can mean a thing you sit up to and eat off or the thing you use to display data.
You also have to take into account the situation you are interpreting in, community interpreting you have to get the message across so it doesn't have to be simultaneous , imagine being at the Dr, you need to know what medicine the Dr is giving you and what dose.
Places like the UN you only interpret into your first language.
There are a few interesting examples of interpreting, one is an interpreter from English into Japanese who said the equivalent of, "The man is telling a joke, I do not know why, I will tell you when to laugh. Laugh now".
Another is from the Vietnam war, a US journalist asks a Vietnamese villager a question, the 'interpreter asks for the villager to count to ten and then gives his (the interpreter) opinion.
Interesting fact for you OP
90% of BSL /English interpreters are women, and out of the 10% that are men 90% are gay.