Is there a regulation that points to not walking on the grass? Or states that all non hand receipt facilities are property of Drill SGT's?

Basically it isn’t a question of property, it is a question of conduct, discipline, and appearance. As a DI it was my responsibility to turn sometimes lazy people with poor posture and socially unacceptable manners into a soldier who can conduct himself properly under all situations.

CPT (Join to see), I doubt there is a regulation regarding these things (a BIG ARMY regulation that is). However, you tagged it - policy.

When I was at Bliss in the early 90s, there absolutely was a post policy letter about staying off of the grass on the parade field when it wasn't used for official activities. Sure, it was about a specific section of grass, but there was one. I know for a fact that Ft. Benning has it as part of their post regulations that you are prohibited from driving on the grass unless it's an emergency (don't think they had anything about walking on it though!).

However, the one thing that a lot of barracks lawyers seem to forget when they start scouring ARs and policy letters on things is that "because I told you so" is in fact a legally binding reason behind an order in the military. Something as tenuous as "it causes an increased wear path because multiple people walk on the grass and it will cost time, money and manpower to regrow it" is a valid military need.

I can't recall any formal NJP (i.e., Article 15) coming out of disobeying the Battalion commander's policy (which I'm sure the CSM put before the 'old man' to sign off on) but I have seen other 'informal' NJP come down -- additional duty on the weekends, being posted as a "grass guard", etc.

Now, the "don't lean on buildings you don't own" ... yeah, that's a bit more of a stretch, but still falls into the category of, "A superior’s order is presumed to be lawful and is disobeyed at the subordinate’s peril. To sustain the presumption, the order must relate to military duty. It must not conflict with the statutory or constitutional rights of the person receiving the order."

Now, I can't envision someone getting an Article 15 for leaning on a building or let alone UCMJ (well, it would be for disobeying an order, not 'leaning on a building'), but I absolutely can foresee some corrective action in that Soldier's future.

There may be local directives concerning walking on unpaved or unimproved areas. These rules are normally in place to prevent folks wearing unwanted, often muddy, paths around the installation. A generalized "keep off the grass" may exist only in the minds of some Sergeants or Officers. Check the installation website. Local directives may be posted there.
A similar observation may be made about the exterior of buildings. The reason for a restriction on leaning against a wall, sitting of a fence, etc., is to protect the property from damage that might happen when hundreds of people innocently stress the facility. Again, check installation directives.