I tend to use all 3 of the browsers for slightly different things so having plugins would be ideal but I suppose I could slum it with copy/paste as long as I follow the password/login route to reduce the chance a password gets exposed.
I forgot about my nexus tablet but android is the other thing to have a look into.
I just save+sync passwords in Firefox and use a strong master password. I (usually) only need to paste the password from Keepass once unless I elect to not save it (such as with financial logins).
> does it work on ios?
Google seems to return lots of results for iOS Keepass apps. You'll want to vet them on your own. I use KeePassDroid on Android and like it well enough.