Does a Buddha see the heart objectively? Does a Buddha or arahant like food and is mindful of that liking at all times or does liking just no longer arise? Does the Buddha like or dislike at the heart level and yet sees the heart objectively?

Related to this question: 
What is the basis?
Feelings (vedana) are of one of these types: pleasant, painful or neutral.

Arahants will experience all these types of feelings.

However, the three poisons of lust or greed (lobha), aversion (dosa) and delusion (moha) will not arise in arahants. Craving (tanha) and clinging (upadana) will also not arise in arahants.

Liking a feeling is basically lust or greed (lobha). So, this does not arise in arahants. They would only endure the pleasant, painful or neutral feeling mindfully.