Let's examine some questions you've raised
Again, even after just doing mindfulness meditation mind and body will tire sooner or later. Simply being awake will tire body and mind. What won't tire is the ability to maintain sati. So I would like to rephrase it a bit and say that "if the ability to keep sati of mind and body are getting tired, something is wrong with the way you are practising".
In my understanding, awareness (sati) doesn't tire body and mind. Its function is simply to remember what is happening in the body and mind.
What tires the body and mind is the wrong
effort that is put in trying to maintain awareness.
On the on the other hand, I am not sure what you mean by "the ability to maintain sati" Is it a thing? How can you know it is tired?
Check your posture;
check the way you are meditating. Are you comfortable and alert?
Also check your attitude; don’t practise with a mind that wants
something or wants something to happen. The result will only be
that you tire yourself.
I think the problem lies in his use of the term "mind". Usually, "mind" refers to many processes such as thinking, reading, body coordination. I think he uses the term " your mind" is a rather different way.
I don't think there's any problem with his using of "mind" here. lobha is a mental factors and belongs to the mind.
Thinking is only one function of the mind, belonging to "sanna" khanda.
Right effort is only possible if the mind has the right
information, if it really understands what right effort is.
We are working towards a goal, but getting to the goal will
happen sometime in the future. Right now we need to know
how to work. We need to know what right effort is and what
right practice is.
A mind which is striving towards a goal, which is focused
on achieving a certain result, is motivated by greed. Wisdom
knows the cause-effect relationships and it will therefore
concentrate on fulfilling the causes and conditions.
I think by "your mind" or "mind" he only refers to the the mind one is identified with while maintaining sati. When sati is present there are two kinds of mind, the one observed and the observing one. "Your mind" refers to the one one identifies with, namely the one based on sati and the processes arising on this foundation. This is the "your mind" he refers to, the "your mind" that does not tire, does not work, will increase it's energy simply by being maintained, and that does not strive towards a goal (at least not in this phase of practice
In reality, there is no person. So what Sayadaw is saying is simply a description of what is going on in the paramatha sense. You can check out the definition of nama, you will see that: vedana (feeling), sana(perception, thinking...), sankhara (mental formations), vinanna (consciousness) all belong to nama. So mind can be one or another depending on contexts.