To perceive and understand science other than as an evidence-based explanation of the natural world would be intellectual dishonesty. Since dishonesty is against the teachings of Christianity, the answer seems clear. This is not to say that Christians should regard scientists as in some way infallible, but it does mean that when a scientific observation is recognised by the scientific community, it ought to be considered as sound science.
I would say as much as possible, because every little bit helps. Apart from that, it would depend on their socio-economic status and general surroundings as to what kind of science knowledge and how much they should know of it.
In general no; it should be capitalized if it's part of the name of something, like a class or department (e.g. the Political Science department).
he felt that science should be used as a way to understand the world
As much as he/she is capable of understanding.
So you can understand science. Almost every branch of science relies heavily on statistical analysis.
Science is interesting, therefore, if you learn about it, you should be interested by it. Only people who have failed to understand science, usually as a result of a haphazard approach that did not prepare them to understand material in a logical sequence, will then be uninterested in the subject.
because they shouldnt
People will always react in line with how they perceive you. So their reaction should tell how they perceive you.
Science is a study of natural phenomenon. It is interesting that some people try to use science to explain supernatural phenomenons. A clear distinction should be understood between science and non-science fields.
A topic that you do not understand. Or an uncomfortable topic that your judges wouldn't want to here.
It is hard for Christians to perceive and understand science because the Bible has very little science in it and religion of any kind is so dogmatic that anything that does not coincide with the Bible's teachings is dismissed as blasphemy, and any person who advances scientific theories is dismissed as a tool of the devil trying to lead good little Christians astray. For what purpose I am not sure. If you can accept that not everyone who has a scientific theory is an agent of the devil, then you might find that there are things that are even more wondrous in science than in God. You have to remember that when it suits them, Christian teachers will either dismiss something they cannot explain as "the work of the Devil, or, when faced with a scientifically accepted fact like the age of the universe, those teachers will blithely say "Oh, yes, well god did create all existence in 7 days...but for him, a day is like a billion years." Come on.