Didn't find an answer from Android Dev Center so I had to stop by in Stackoverflow to find few answers...
a) Will my app get rejected if I have different icon for launcher image and Google Play store, ie. Google Play store icon will have text on it, whereas launcher image will not? Small modification will also be present.
b) Can I somehow have different app icon and app name (the one that shows in Google Play and under the launcher icon) depending on language, ie. for English and Finnish?
a) No. There are many kind of apps that doesn't show an icon in launcher, for instance, App Widgets or Live Wallpapers so I guess there are no strict rules about it. However, if the icon on the Play Store identical to the launcher icon, users can easily find your app on the Play Store so those should be same to increase a findability.
b) Yes and No. You can have different app name for each language, in app resources and Play Store listing details. You can also change the launcher icon by putting it into res directory with a locale qualifier, such as drawable-en-xhdpi. However, Play Store doesn't support changing the icon depending on language.
Edited: Now Google Play Store supports using different assets for each locale, so you may specify localized icon individually.
The exact answers of your question can be provided by the google authority. But let me try to share my findings regarding your questions.
a) I haven't found any info like this in the googleplay policies here and here. But In this link in one place it is written that
The assets should reference the same logo and icon as users will actually find in the All Apps launcher once they have downloaded the app
So we can conclude that it is must to use the same icon. Although I don't know how they check it.
b) So far there is now way to do that. No info like title, description, images can be set differently for different language ( someone corrects me if I am wrong ). You can do one thing. For different language you can publish different apks with different package name. By searching you can find similar problems. this so question is one of them.
You can Also check Multiple APK support in google play. Although it is targeted for different devices you can check whether the same things can be done for the different languages. (I am not sure about this :S)
