Is there a way to move the ...

[rickap7]

+(add contact) icon in contacts as well as the icon in messages to start a new message and others with Lollipop?

 

[Rukbat]

Only by rewriting the Contacts app (which not many people [like maybe 100 in the whole world] would be interested in getting involved with). It's MUCH easier to write an app than to read the mind of the developer who wrote it so you can change it (And with most apps, that's what it would take, after they're decompiled - which is reverse engineering, which one can be successfully sued for doing.)