Is there a way to recover contacts and T Memo from touch broken galaxy core
You can use an OTG cable to connect a mouse to the phone that will give you full access to the device.

You will then be able to go into contacts>settings>contact settings>export contacts, and select your desired method. I would suggest you export the contacts to an sd card, put it in into your new phone, and import them.

You should be able to do the same thing for your memos. Export them to an ad card, or save them to a cloud.