They do through their shop on Rakuten Global.
A friend of mine had the same problem with hers in similar conditions.
I think in cases like that it’s probably okay to use them in a light drizzle, but not heavy rain. The biggest problem I’ve heard of with their parasols is that they rust so just be sure to take care of it and if you do use it in the rain dry it with a towel before putting it away.
Some are and some aren’t. It looks like all the ones they have in stock right now are. It will say specifically on the page “For rainy and sunny” if they are.
A fair number of brands that make parasols have them waterproofed so they can work in rain. Not all of them of course, but if they’re waterproof it’ll usually say on the item page. My Innocent World parasol is waterproof and I’ve been using it for a year with no problems. I know that most of Lumiebre’s parasols are waterproof too. Keep in mind though that when ordering a parasol online you’re taking a risk that it may be hurt during shipping. That’s the reason Bodyline doesn’t sell them overseas anymore and it’s why umbrellas like this are great because they fold down small so they’re easier to ship and harder to damage in the process. That isn’t to say that you shouldn’t buy a full sized one if you find one you like, but keep in mind that there is sometimes a risk of damage.
They used to but I don’t think they do anymore. I believe they got rid of them because they almost always got damaged in the mail when they were ordered by people outside of Japan and they got a lot of complaints because of it.
Bodyline doesn’t sell them overseas anymore due to them getting damaged in shipping. If you want one cheaply and quickly that you can be sure is waterproof, the easiest thing you can do is to modify an umbrella yourself. I recommend this because most of the other parasols I’m finding that are inexpensive aren’t made to stand up to rain.
I really like Innocent World’s parasols. I’ve had mine for a few months and have used it in pretty heavy rain and it’s still in perfect condition. The best part is it’s collapsible so I can fit it in my medium-large purses. Lumiebre has great parasols, many of which are waterproof, but they’re a bit pricy. A few brands sell parasols that work in the rain, I would just look for reviews before buying to make sure.