I'm actually doing a master's in the history of photography (more or less), and I have a professor who specializes in the early days of photography in the press. Halftone was definitely coming into use in the 1890s, as has been noted. Other methods of photomechnical reproduction were around too, though they were a bit more labour-intensive and costly, so used more often for books and/or magazines. A person could easily be a professional photographer at the time-- I'm not actually sure if newspapers had photographers on staff specifically yet or not but they certainly would commission photographers (who might have made a living elsewhere). Newspapers were hiring photographers from the early days of the medium (1840s), even when photographs couldn't be reproduced mechanically-- as noted, they had engravers on staff to interpret the photographs. This was a really common thing, so there may very well have been photographers who specialized in news even in the 19th century. I could probably track down resources that would give a definite answer-- let me know!
As snafu mentioned, Kodaks were around in the 1890s (they came out in 1888) and were a pretty fast, lightweight camera for the time-- however, fast for the time means to take an actual "snapshot" you would need direct sunlight. Otherwise you could make a timed exposure using tables (this was still true for cheap Kodaks in the 1920s-- I have a model myself). But a professional photographer in the 1890s would not be using a Kodak for his work. They were purely a toy. A professional (in any area of photography) would be using a view camera (
http://en.wikipedia.org/wiki/View_camera), a big bulky thing on a tripod. For professional work it is unlikely he would be using film-- probably he would be using glass negatives (heavy and large--they are the same size as the final print, so if you want an 8 x 10 print, you need and 8 x 10 sheet of sensitized glass). These were the norm in commercial photography into the 20th century. All this of course takes a while to set up and to move; the taking of photographs was a very different process than it is now.
He could definitely take pictures in the rain though-- he'd almost certainly need an umbrella to keep his stuff dry, and it would be a long-ish exposure, but sure. This photograph was taken in snow in 1893:
http://www.metmuseum.org/collections/search-the-collections/270042 .
I am happy to help with any more specific questions, just message me. If there is a certain outcome or scene you want, I can help you tailor what he does in photography to suit it, too, if it was possible at the time.