Most effective way to backup contacts from iPhone to plain .csv - format
If your contacts are stored in iCloud, use this method: 


Go to iCloud.com and log in with your Apple ID
Click the Contacts web app
Highlight all contacts (click the first contact entry, scroll to the
bottom of your list, hold the 'shift' key and click the last contact
entry)
Click the 'Settings' icon in the bottom left hand corner of the page
Select 'Export vCard'


The vCard should now be in your '~/Downloads' folder (if you haven't changed the filepath for new downloads from your web browser settings)

If you own a Mac (and it appears all of the contacts from your iPhone are also accounted for on your Mac) use this method:


Launch the Contacts application
Highlight/click a contact
Select all ('Edit > Select All' or press 'command + A'
Click 'File > Export vCard' and save it somewhere safe


Now you will just need to find a conversion tool to convert the vCard (*.vcf file) to a *.csv file. There are many free online options such as this one but I cannot attest to whether or not the online tools are secure (as in, I don't know if they store your file on their servers somewhere after the conversion process and if they can access the information for your contacts). 

A safer option would to go with an actual application that doesn't send the information to any website servers to convert it. If you have a Mac I found one on the App Store that looks promising called vCard Editor for $5.49CAD but I personally have never used it to know how well it works.

As for backing up the Notes, you're not going to like the answer. Just remember - don't shoot the messenger!

There isn't a way to backup all of your Notes at once from an iPhone or iCloud.com. (What was Apple thinking?!) The 'Apple approved' method of backing up your Notes is to either email or text (SMS) each individual Note to yourself from your device. Yes, I'm being serious. This is even the method they walk you through if you call Apple Support for assistance.

Fortunately if you have a Mac and all of your iPhone notes appear to be accounted for on your Mac as well, there is a work around (although it will not be in *.txt format). On your Mac you can copy the '~/Library/Containers/com.apple.Notes/' folder to someplace safe in case you ever want/need to restore all of your notes at once. 

Note: The copy/backup of that folder that you make doesn't update as you add new notes or delete some, so if you ever do need to restore that file you need to copy/backup all of your new notes first otherwise they'll get 'over-written' (for lack of better terms) upon restoration of that folder.