1) You cannot accept an OTA while rooted. The fact that you have a custom recovery prevents it. Even if you replace it with the stock recovery, it's a really bad idea.
2) What exactly did you remove? You should always be careful when removing things like that. If you want to remove it, you should do so with something like root explorer, and just rename the extension from apk to bak. Otherwise, just freeze apps. None the less, if you wipe cache/davlik/data and flash any ROM of your choice, everything will be fine. Whatever is or isn't working in the current ROM doesn't affect flashing a new one (assuming it's a complete, working ROM that doesn't depend on anything currently flashed; most ROMs are fine).
3) What are your current hboot, radio, and software versions? If you need to catch up on updates, you should update manually. You'll need to before just flashing any ROM updated to the latest software version.