Can you 关心 an object? So, I've used 关心  consistently with people -  关心别人， 关心我的妹妹，  but can 关心 be used for object or a phrase?? 

Example for a phrase 
我们关心的应该是房子应该有几间屋子? 

Example for an object 
吃饭时， 我关心的是调味。 长得怎么样， 我都不管。
Yes, you can.
Oxford

VERB
care for
关心国家大事
be concerned about the major issues of one's country
双方共同关心的问题
matter of mutual concern

You above sentences have some grammatical problems but using 关心 in this manner is no problem.