Many people are experiencing phone turning on after turning off. One solution is put phone in sleep mode rather than full power off. That seems to work.
On Market problem, try this. In menu, manage apps, go to market. push "clear data" or "uninstall updates". Next time you go to Market, you'll be using the default version of Market app, but it will automatically download the update. Close market, wait a minute or so for the update to install automatically, then go back to the market. Should work. There are cases where automatic update available notification is bypassed (to avoid nagging to update an app you don't want to update). First, make sure you have the app backed up (using Astro file manager backup function, or back up with some other app). Then install the update from the market. Then uninstall that app from the market. Close market, and restore the app from your backed up .apk file. This will restore previous version of app, leave the app in the Market list of installed apps, but remove it from the UPDATE section in Market's display.
On keyboard problem, go to menu, keyboard and language, multi-touch keyboard settings, and uncheck auto-correct, auto punctuation, and whatever other automatic actions might be causing the keyboard to seem to be acting on its own. Also make sure you didn't install some third party keyboard app
On Market problem, try this. In menu, manage apps, go to market. push "clear data" or "uninstall updates". Next time you go to Market, you'll be using the default version of Market app, but it will automatically download the update. Close market, wait a minute or so for the update to install automatically, then go back to the market. Should work. There are cases where automatic update available notification is bypassed (to avoid nagging to update an app you don't want to update). First, make sure you have the app backed up (using Astro file manager backup function, or back up with some other app). Then install the update from the market. Then uninstall that app from the market. Close market, and restore the app from your backed up .apk file. This will restore previous version of app, leave the app in the Market list of installed apps, but remove it from the UPDATE section in Market's display.
On keyboard problem, go to menu, keyboard and language, multi-touch keyboard settings, and uncheck auto-correct, auto punctuation, and whatever other automatic actions might be causing the keyboard to seem to be acting on its own. Also make sure you didn't install some third party keyboard app