Just to clarify, what you have tried :)
The First try ($wgMobileFrontendLogo = "{$wgScriptPath}/mw.png";) will try to load the image from your wiki's script path (there, where the inedx.php is, probably the wiki root). That won't work, because you uploaded the image to extensions/ not into the wiki root :)
-> Solution for this way: Change in LocalSettings.php to: $wgMobileFrontendLogo = "{$wgScriptPath}extensions/mw.png";
The second ($wgMobileFrontendLogo = "/images/mw.png";) tries to load the image from the absolute server path (important is: absolute path). So, if your wiki installation is at /var/www/wiki/ the server tries to load from /images which is an directory at the same position as /var. This is impossible, too, because you uploaded the image not to this absolute dir.
-> Solution for this: Change the value to the solution of first one, or (if you want to upload the image to images/ of your wiki) then do:
- Move mw.png from extensions/mw.png to images/mw.png
- Change in LocalSettings.php: $wgMobileFrontendLogo = "{$wgScriptPath}images/mw.png";
The third ($wgMobileFrontendLogo = "$IP/extensions/mw.png";) is the most false way :) $IP is the absolute path to your wiki installation, e.g. /var/www/wiki/. The Browser will try to include the image using an relative path which results in an construct like: http://example.com/wiki/var/www/wiki/extensions/mw.img. This can't work :)
-> Solution: Use the solution of the first one ;) $IP is, simply said, only for installation of extensions or skins.
Hope that helps you!