Yeah the workaround is to use “search web” function through the dictionary and then copy the text from the search box.
The ones in my screenshot with the cloud icon aren’t downloaded. And your library doesn’t even have to show up on your bookshelf at all. So you can only download the ones you’re reading.
Like @rodan mentioned, the free ones are usually only available for a limited time. On the app, when that happens, tapping on it takes you to the store page.
I’ve been watching way of the househusband on netflix. For a premise that sounds so boring, it’s actually kind of entertaining
dlsite has a manga/light novel section:
As the name implies, everything can be downloaded to your computer or phone. It also has a translated english user interface, which might help. 
And they have sample pages, so you can quickly check if the level is to high or not.
Starting off, shoujo mangas might be best. (Since they are closer to everyday japanese than shounen and don’t go to crazy with the kanji)
I thought DLsite is just for umm… you know right?
but does Yomichan do OCR? The app i linked uses OCR to extract the text from images
for japanese pc games. ;D
But yeah, they have expanded.
Yeah! yeah… lets go with that
hehehehe I see what you did there.
But hey - reading is reading. Right?
Yeah I can see now that’s useful, but it’s just not the problem I have. 
I never read on my computer.
Visual novels for the cultured consumer. 
Oh yeah, お兄ちゃんはおしまい is also released on there. I buy the volumes to support the creator and get the bonus chapters, but I think you can read the whole series on Pixiv.
Might not have a lot of up-front free stuff of one and the same manga, but https://kodansha-cc.co.jp/ and https://mangacross.jp are two publishers that are great to find new manga with. The latest chapter(s) are usually free and you can use sites like https://webcomics.jp to keep track of when a new chapter is released. It also nice to discover even more manga. if you look around on any of those sites, there are also some entirely free manga or some that didn’t start too long ago and have loads of free chapters.
If you you are not fan of spending money,
comic-walker.com site is the official site with free comics of KADOKAWA publisher.
You can also read web-novels, e.g. re-zero (Not, it’s web novel version, not LN, LN version is not free)
It seems to definitely depend on the particular artist whether they post everything there or not, but there’s certainly an endless supply of reading material.
For amazon.co.jp, I use the Japanese address that tenso.com game me. Tenso is a forwarding service. Japanase stores ship the stuff to “your” Japanese address at the Tenso warehouse, at the normal local (usually cheap) shipping rate; then Tenso ships the stuff to your home address, at hella expensive international shipping rates. You can use any Japanese forwarding service; there are many.
A good forwarding service will allow you to consolidate many packages into a single box, for which the shipping cost is usually cheaper than shipping each package individually. But watch out; if the aggregate box becomes too big or too heavy, then it hits some FedEx/EMS/DHL threshold and becomes super stupid hella expensive.
Eventually, you will probably one day want to pay that hella expensive shipping for a physical item from a Japanese store. So it doesn’t hurt to setup a forwarding service now. A Tenso account is free; I don’t about others.
We’ve recently had flags related to people linking to websites with pirated material here, so just want to ask people to be mindful of Goal 5 here when pointing people to resources and such. Thanks everyone!
The problem is that I think people are not aware that the website in question is illegal. (In fact, I’m 100% certain it is pirated contents myself, but it’s still just looking like a very very black shade of gray)
100% legal and free webmanga site:
Many still ongoing stories, but also a lot of completed ones too if you just want to binge:
My personal favorites are as follows:
But there’s a lot more to choose from. The best part is, on each manga’s page there’s a link to the author’s Twitter, where you can (sometimes) find links to other stuff they’re working on.