1. Juicebox-Pro 1.5.0 gallery Thumbnails image look like blur image
It looks like the thumbnail images on your server are 85px x 85px and your gallery's configuration file does not entries for thumbWidth and thumbHeight so the thumbnails should be displayed at 85px x 85px (the default values) so everything should be OK.
However, your screenshot ('image1.png') shows the thumbnail images being displayed at a different size (maybe something like 100px x 85px). It looks like your mobile browser might be using an older version of your gallery's configuration file (one with a custom entry for thumbWidth).
I have viewed your gallery on my own mobile iOS device and your thumbnail are displayed at the correct dimensions (85px x 85px) so it looks like the problem may be your browser's cache.
Try completely clearing your mobile browser's cache before reloading your gallery's web page.
This should hopefully solve your problem.
2. i want
gallery index page -> full screen image
Set showSplashPage="NEVER" (in the 'Splash Screen (Pro)' section) to disable the Splash Page.
You may also like to set showSmallThumbsOnLoad="FALSE" (in the 'Thumbnails (Pro)' section) to initially skip the thumbnail page in Small Screen Mode and go straight to the first image in the gallery when the gallery is loaded.
Alternatively, you could set screenMode="LARGE" to force the gallery to be displayed in Large Screen Mode in all browsers and on all devices. (Large Screen Mode does not use the Splash Page by default.)
For more information about Screen Modes and the Splash Page, please see here.
3 fixed forwarding -> resolve thx
That's great. Thank you for letting me know.