OS X and firefox, gmail, add-ons, incompatible?

Since I know there's a lot of knowledgeable people out here I am going to ask you for help or advice on two more two more issues which I can't comprehend:

I have a MacBook Pro, Mac OS is 10.6.5, Firefox 3.6.10.
Here's a list of my problems that really drive me crazy and have not been able to solve this - something I never had to deal with on a Windows system:
(btw. I have reinstalled all the software and have updated it to the most current versions).

1. Google email has often problems in Firefox in the sense that when I look up an email (say an email that contains several responses) I often end up not being able to scroll down to see the whole content of it. When this happens, two vertical sidebars appear on the very right of the screen - seems that one vertical bar is within the very email thread whereas the other is for the whole window. But no matter how much I manipulate with either of them, I just can't scroll down to see the whole content...the page just seems to be cut off...weirdly enough if I hit "enter" several times, even the cursor disappears while the text does not appear.
This has never happened in Safari or Google Chrome.
In Firefox, it's become a total feature of my browsing experience (happens virtually all the time...i.e. can browse my gmail account normally for a while and then, for some reasons, this problem occurs). A solution to this is to restart Firefox. Then everything is fine for a while.
I have been searching for a solution/or a similar experience on the web but have not been able to find the reason for this?

2. So why not switching from Mozilla to Safari or Google chrome? Well it's connected to a software that I use on a daily basis and that has been designed for Firefox only - it's called Rikaichan (a super cool Japanese dictionary..I read Japanese everyday in my work). This add-on has been designed for Firefox only (works also in Chrome, but badly...really badly, that's why I can't switch).
And here's a second problem, again appears only in Firefox>

I often switch between English and Japanese keyboards (have both options set in OS X preferences as my keyboards). But when using Firefox after a while the option of Japanese input suddenly disappears from my OS keyboard bar (i.e. when I click on the keyboard icon, only English keyboard is available). When I restart Firefox, it works again just fine (for a while).
This problem occurs with total regularity, though I can't really pinpoint what the causes to these are. As with the previous system, I have tried to search on the web but was not able to find anyone who would complain about this.
Btw. the keyboard option never disappears from other applications - i.e. when I switch to e.g. Chrome, I can use any keyboard I wish.

This only explanation i have is that somehow the add-on rikaichan is not compatible with Firefox? And that it causes both the problems with the keyboard and google gmail viewing? But how? It actually makes little sense. Also because I used to use Rikaichan before and had never a problem of similar sorts.

Any idea how to solve this? Obviously, as long as I don't have a replacement for Rikaichan (Rikaikun on Chrome doesn't work for me) I need to keep using Firefox. But this really drives me nuts...recently I have been restarting Firefox several times within an hour.


Thank you for your input,

Christina