Some observations and pieces of info, in no particular order....

• To tell FileZilla to upload only new or changed files, go to Edit, Settings, Transfers, File exists action, Uploads, and choose Overwrite file if source file newer. That will save you a boatload of bandwidth and time.
• The uploading process doesn't create any files. Whether you're using FileZilla or the jAlbum uploader, it's just a file copying operation. No magic is taking place.
• The index.html file is created when you make the album, and is the top-level file of the album (and of each folder in the album). It exists in the output directory when the album build is finished, and then gets copied to the server along with everything else. But yes, if it gets deleted, you get no album when you try to view from the server.
• jAlbum doesn't create an ext directory, so there's no telling where that's coming from - it's not part of the album structure.
• When viewing your album, and looking at what's in the developer's console in the browser, I'm seeing all sorts of server errors. They show up as 500 errors, which translates to "server configuration error." This is a problem with your web host - it's not something you have done, or even could have done. To look at this info in Firefox, go to your page. Then hit F12 to pull up the console. Go to the Network tab. Click the little trash can at the left, then click the word Reload.
• Your image files seem to be on the server, but because the server is misconfigured, they're being fed to the browser in the wrong form. For example, simple JPG files should be served with a MIME type of image/jpeg, but yours are arriving at the browser as text/html, so the browser doesn't know what they are. Firefox doesn't know that it's a picture, so it's just lost. This is also revealed in the Firefox developer's console. Again, this is purely a web host issue - it's not something you can fix.

In short, this has all the earmarks of a web hosting problem, and you're sort of stuck with working with them to straighten it out.

I have a hunch about what's happening here. Because of impending changes in European copyright law, web hosts are going to be saddled with responsibility for violations, rather than being able to say, "we're just a host - complain to the person who uploaded the copyrighted material." I'm guessing that your host is now scanning all uploaded files, to make sure the material isn't copyrighted, and they're making a mess of the process. This is just a guess on my part.

If the EU goes ahead with this thoroughly bone-headed plan, it's going to put all of the smaller web hosts out of business, because they can't afford the overhead needed to check every uploaded file. That will leave only a few giants, and with no competition, prices will rise and service will head for the basement.

The future of jAlbum hosting is, in fact, threatened by this change - jAlbum is a small company, and if it got hit with even a single large copyright violation problem, they'd be out of business.

Call and write to your government representatives. Make sure they understand the carnage they're about to unleash.

You could flee to a U.S. host, but if most of your site visitors are in the U.K., that might not be very satisfactory. That transatlantic hop will always slow down response times (that's why I don't host on jAlbum - it's just too distant). Then again, it might be fine. Try https://jgromit.com/ - that's coming from a server in Denver, Colorado, two-thirds of the way across North America.

I have deleted a number of confusing, irrelevant tangent posts in here.

Let's not confound the issue - the original poster needs to contact the web host to determine why simple file requests are producing 404, 500, and 508 errors.