While you didn't exactly verbally spell out he was on a probationary period. (Very common circumstance,, Most farmer's don't approach hiring some one the same as going into a partnership/LLC. ie: no exit stratagy explicitly spelled right in the begining)   You did state a "probationary wage"  

 "I told him that I would pay him Y dollars/week and after 6 months if he was what he said he was, I would gladly give him a raise."

Well simply stated,, he is not what he said he was. 

At this point, All you have to do is tell him exactly what you've said here.

1.   He is the last one to the shop in the mornings, first one to leave in the evening,
      (Manager's are worthless as T*&$  on a boar!   A Leader is the first one there and the
        last one to leave at night. People are "lead" not Managed)

2.   You didn't list the lies,, but spell out exactly  which tasks or knowledge he professed 
      to have but does not.

3.   Far as "spending your money".... He is being paid to "think" in all fairness. So in that 
      light, if he sees an opportunity to improve something,,  He should point it out to you,
      HOWEVER,, it  is up to You and should only be up to you to decide if his 
      idea/suggestion has merit.   *would you NOT want an employee make a suggestion if
      they saw and/or knew something which would improve your operation??,, remember 
      everyone has different experiences knowledge to bring to the table.*

HUGE piece of Advice here,,,,,    "Tell him that you feel for the operation to.."

LEAVE ALL THE 'FEELINGS',, emotions, 'I think' and all that inter-personal, 'I think, I feel,, etc'   out of your converstaion COMPLETELY!  

Talk to the guy using cold hard facts about his performance. Absolute's when talking about tasks or jobs not being done.  Such as showing up.....   " I feel you should show up first and leave last."    Completly Wrong tack to take,,, You just turned the conversation into a "touchy feely personal emotion" conversation, ABOUT YOU AND YOUR FEELINGS...   You really want to Lead people that way?? 

*much better way to say the same thing* 

  "As a first level supervisor, how you conduct yourself, when you show up and when you leave sets the example for all the other employees.  You show up last, leave first, and that is the WRONG example for a Supervisor to set. This business depends on employees showing up on time when expected. As a supervisor when YOU DO NOT show up on time, YOU are setting a bad example for those you are supposed to be leading. This behavior is not, will not, be tolerated in this business." 

It is a simple concept actually..  stick to facts, make the conversation about him and his performance (or lack there of..)  AND most importantly,,, leave all the 'touchy-feely-emotions,, 'I FEEL' statments completely out of the conversation.

Seriously,, it's not hard to fire someone,  IF,, you stick to absolute known documented facts and keep the conversation about him and his performance or lack there of. 

Leave out your anger, frustration, feeling's, apprehension, etc..  simply state facts as they relate to the job.