I tried to use some jpg files for title image and battle back image. It will show file not found for *.png
It looks like the engine only takes PNG files?
The issue is that if you don't use transparent images, PNG usually generate unnecessarily larger files than jpg.
The editor doesn't support it because it leads to people shipping broken games. You should not be using lossy images in a 2D game. PNG is required due to the transparency necessity. Allowing the user to select any arbitrary image means users will ship games that don't work as expected on all advertised target platforms. The backgrounds are layered so they do in fact have transparancy. Note the difference between battlebacks2 and battlebacks1.
No Japanese game out there prefers lossy image formats. Even going back to PC98 systems. Older games used masking files (the character generator uses them too) to allow fake chroma-key images, but the real benefit with PNG is how you can use transparency as transparency and not resort to "every other pixel" fake-translucency tricks.
If would be a different case if the editor actually did the compression itself to make it idiot-proof.
Now, as to how to make PNG files smaller without wrecking them,
OptiPNG ,
PNGCrush ,
AdvanceCOMP do a fairly good job, often saving 20% by eliminating the unused chunks if you tell it to. However it is entirely possible to wreck the PNG files by over-optimization, as some optimization will remove transparency, or reduce the colors from 32bit to 8-bit palette without prompting, or even crop the image.
However be aware that just because you can fool the editor into accepting things like JPEG, GIF or WEBP, doesn't mean that the game will work on all devices, or at equitable performance with all formats. PNG was created to get people to stop using GIF due to the patents on the LZO algorithm (which has since run out) , however because people try to create animated images with GIF, APNG or WEBP, they will be upset when they don't animate in the game engine. The game engine uses CANVAS, not the browser image tag. So these files are being treated the same as single uncompressed 32bit images regardless of the file compresssion used on disk.
The same thing can be said with the audio. Just because the OGG Vorbis(OGG) or AAC(M4A) audio is there, doesn't mean it only takes up 3MB of memory, no it takes up to 64MB of memory if it's 10 minutes long regardless of the compression used. Hence you should trim and loop audio tracks rather than have 10-minute long tracks. Both of these formats are lossy. It is possible to store lossless audio in both containers, but they don't have PNG-like compression.
Anyway it's a major nitpick... only use PNG in your games, it will be less frustrating for you later.