as the others said -- welcome.
if you are having problems, a factory reset is always a good thing to try. often there are other options to fix a problem, but factory resets can often fix issues you are having.
as far as the gmail issue, go to settings -> battery manager -> battery mode, and make sure you are not in a battery mode that is disabling data from coming thru. i highly doubt that is the issue, but the default setting stops email from coming in at night to save battery in case you dont have it on the charger.
second, go back into the main settings menu, and go to the data manager section. make sure all three checkboxes are checked.
last, go to my accounts, and remove the gmail account altogether (long press on the account to delete it), then try re-adding it. the reason i suggest this before the factory reset, is because if you arent getting emails, there is a chance contacts arent syncing either.
the text message issue is a common thing. moto "says" there is a fix coming for it. try downloading handcent. it is better than the stock messaging app anyway, and the newest release seems to have fixed that for me. i doubt doing a factory reset will fix this, so if your email has been solved by now, i wouldnt do the reset.
finally, if your email still isnt working, to do the factory reset:
menu -> settings -> privacy -> factory data reset.
doing this will wipe your phone to out-of-the-box settings (but on 2.2). when you log back into gmail, contacts will come back. if you have paid for any apps, you will have to download them again, but you wont have to pay.
ps, there is also one other way to do a factory data reset:
while the phone is off, hold the home button, then power on. let go of the home button after about 5 seconds, and you should see a little logo on the screen you havent seen before. hit the search button, and it will bring up a list of options. you want to select the one that says something like, clear data. you can scroll up and down with the menu buttons, and select the one you want with the camera button. if your phone ever seems wonky, sometimes just clearing the cache can help.
i hope this wasnt too long and boring (if you even saw it), and i hope it was helpful. i know the guys before me gave you some great answers to the questions, but i wanted to try to hit it all in one stop instead of linking you all over the place.
pps. as for rooting, it's an android/linux term that basically means you have administrator privileges (in windows terms). see, android phones dont allow you to access system files. so beyond just installing apps there, it doesnt allow you to alter anything else. root allows those things. so, there are apps out there (like wireless tether, screen capturing apps, apps that allow you to monkey with the processor's clock speed, etc.) that need to be able to change system files, and being "rooted" allows that. it also allows you to eventually do other things, like change the way certain things look, like fonts, status bar color, status bar icons, etc. those are things you may learn down the road, but like it was said before, the root section of this forum is an awesome place to learn about all that stuff. but on that note, if you feel like you dont understand something, dont feel like you shouldnt ask, just because it has already probably been talked about. any questions you ever have, dont hesitate to ask here.
good luck, and happy droiding.
I love my phone. but it confuses me. And Ive had some issues that Ive seen a lot of other people have had since i updated to froyo. 
