Welcome to AF! Glad you made the jump from iOS to Android
Not sure what your phone offers out of the box, but there are a few 3rd Party apps that could do what you're asking.
1. What sort of notifications are you talking about? For emails/SMS or any other apps? I use Widgetlocker
for my lockscreen along with Tesla Unread
. If I've shortcuts for Gmail, Talk, SMS on my lock screen, Tesla will display the number of notifications/emails etc in the corner of each app. See here
. Alternatively, Not sure about Gmail/Talk, but the 3rd Party SMS can display a pop or notification of your message on the lockscreen too. Look at Handcent, GoSMS, Pansi SMS, see if they are to your liking.
2. Again, not sure what your options are on stock, but using an app like SMS Enhancer
should let you achieve what you're looking for.
Let me know if those help, if not, I'll dig about and see what I can find.
Edit - I took ages to type, it looks as though DC got in before me. There's enough suggestions in here to hopefully put you on the right track, shout if you get stuck though.