Japanese keyboard assistance needed

Greetings all.  Yet another beginner question for anyone that can help.  I'm a linux user and have been using IBus/mozc input for hiragana, however it appears that this does not work within web browsers.  I have seen hiragana stickers for qwerty keyboards and am under the impression english qwerty keyboards can be used to directly input hiragana?  While typing out romaji doesn't bother me, I would find it preferable if I could directly input the hiragana.  In my mind, I see it as a good idea to break away from the roman characters and train myself to "think japanese" when it is possible. 

EDIT:  To answer my own questions. After tinkering around, I found within mozc's japanese input settings you can change the input method from romaji to kana.  This allows the direct input of hiragana I was looking for.  The trouble with firefox and chrome web browsers is a current bug that has broken the IBus IME.  Switching over to the Opera web browser has solved this problem.  Slim chance, but maybe this information will help any other linux users having similar problems.

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Hiragana double consonants and dropped vowels? Greetings all, this is a very beginner question.  I've recently taken up learning Japanese and decided to avoid romaji as much as possible.  So, before beginning any real studies I felt it was important to get a firm understanding and acceptable reading speed of the kana.  I have all of the hiragana and individual pronunciations down.  However, I'm having a hard time grasping the pronunciation of double consonants and the rules regarding dropped vowels.  I kind of assume dropped vowels are a case-by-case thing and will come with learning the vocabulary?  Not having any audio aide for the double consonants is causing a little difficulty for me though.  For example, "katta" and "kata" I read both the same way (or guessing katta may be pronounced kah-tuh and kata kah-tah).  Can anyone point me in the direction of a good source for gaining a thorough understanding of either of the above subjects?  Thanks ahead of time for any help : )