The meanings of the two terms largely overlap. Frankly, when they are used together, I think it's pretty much a redundancy for emphasis. If you asked a salesman, "What are the most important features of your product?" versus "What are the most important features and characteristics of your product?", I would expect you would get the same answer either way.
We do this a lot in English. Sometimes a single word just seems too abrupt. So instead of saying, "When the letter arrived, Sally was happy", we might say "When the letter arrived, Sally was happy and joyful." Instead of just saying, "Bob is irresponsible", we'll say, "Bob is lazy and irreponsible." Etc. Sometimes the extra words arguably do add some shade of meaning, but often people add extra words that mean pretty much the same thing just for emphasis: instead of saying "she was very very happy", it sounds more literate to say "she was happy and joyful".
You wouldn't normally talk about the "features and characteristics" of a person. This is a phrase used to describe inanimate objects, usually some machine or gadget. If you asked, "What are Mary's features and characteristics?" it would sound quite strange, like you were describing here as a product that you were going to sell.
When talking about a person, "features" means his physical appearance. If someone asked, "What did you notice about Charly's features?" they would expect an answer like, "He has brown hair and a scar on his left wrist." Similarly if you ask about the "features" of a place, like, "What are the features of the Toutle River Valley?", they would expect you to describe physical (geographic) features, like "There's a hill on the north end, a deep gorge running most of the length," etc. But if you talk about the "features" of a product, you normally mean details about how it functions. If someone asked, "What are the main features of your new Whizbang 300 cell phone?", they wouldn't expect you to answer, "It's black and sort of rectangular", but more like, "It has a built-in GPS and a function to mask out background sounds when you call your wife from the bar."
If you talked about the "characteristics" of a person, that could mean anything about him, from "He has blue eyes" to "He is an excellent basketball player." I suppose you wouldn't use "characteristics" to describe something very temporary, like "He is sitting at his desk"; it would normally be used only to describe a fairly long-term attribute.
(Whew, that answer was longer than I intended.)
Best Answer
That's a very tricky problem.
On the one hand you don't want them to bump into you, on the other hand cultural norms (here in South-East England) forbid you from invading the privacy of strangers by speaking to them - or, god forbid, even perhaps startling them, which would be rude.
I would cough loudly to make them aware of my presence. If they're actually moving in your direction and are inches from hitting you then a "sorry!" is culturally permitted. "um!" or "ooh!" is also a last-minute option. As @Andrey suggests, "behind you!" would also be ok if a collision is otherwise unavoidable.
If you are actually bumped into then normal usage is for you to immediately apologise ("sorry!"). You can pre-empt this a little bit by acting as though the collision has taken place when actually it's about to take place ("sorry!"), thereby preventing it from taking place.
I believe that in other English-speaking countries around the world, the problem does not exist (or not to this extent), and a cheery "hey there buddy, mind you don't bump into me!" may be allowed.
Rather than trying to say something, a simpler option may be for you (as potential bump-ee) to silently take evasive action.
If you're riding a bicycle then two dings are appropriate,
Towpath cycling code of conduct, British Waterways
although remember to look embarrassed and say "sorry!" or "thanks!" as you pass, in order to soften the "undertone of reprimand":
One cyclist's bell has turned into hell on the towpath, Ben Thomas, The Guardian, 22 Oct 2009
If you're driving a vehicle and a pedestrian is about to step backwards into the road and be run over by you then it is permissible for you to toot your horn, but expect them to be annoyed at your rudeness rather than grateful that you've saved their life.
Anthropolgist Kate Fox has conducted extensive experiments in the bumping of English people:
Watching the English, The Hidden Rules of English Behaviour, Kate Fox, ISBN 0340818867
However, the 'you've just bumped into me' "sorry!" is not necessarily a sincere apology:
A Poor Apology for a Word, Henry Hitchings, New York Times 13 Dec 2013
Of course none of these shenanigans are necessary or desirable in other parts of the British Isles, or even in the North of England, where all this ritualised politeness is often perceived as an affectation of effete middle-class Southerners.[linked video contains swearing, may be NSFW]