Hey! I can’t speak from personal experience, but from what I've heard about LAET, the uniform policy is kind of flexible but still formal enough. Smart trousers should be fine, and for shoes, maybe try loafers or something similar that's not too "smart" but still fits the dress code. Trainers are usually a no-go, but as long as the shoes look neat, you should be good.
As for the shirt, yeah, tucking it in might be required for that clean look, but honestly, you could just check with someone there or see how strict they are about it.
And about being alone, I feel you! Sometimes it's like that at first, but you’ll probably find your people soon enough once things get going. Don’t stress too much!