Here is the situation. I tried asking this question on Macrumors but no one could help me.

I want set up a Raid 1 array with my MBP laptop's internal hard drive and an external hard drive. I want to leave external at home and only take the laptop on the go.

Can I do that, will Raid help me update by itself when I remount the external hard drive when I come home?

If not, is there something that is automatic that I can use to back up my data in the laptop?

Thanks

If you have your external an a USB enclosure then it should show up whenever it is plugged in. There is no need to create a raid array.

Can I do that, will Raid help me update by itself when I remount the external hard drive when I come home

No, thats not how RAID 1 works.