The lease will be in you and your partner’s names and must be honored. That means that if you want to quit the lease you will have to abide by the lease terms for termination and may be liable for rent until such time as a new tenant can be found.
There is no formal receivership process for partnerships in the way that there is prescribed process for corporations (which is set out in the Corporations Act). Presumably, when you appoint the receiver you and/or your partner will be giving the receiver instructions to realize the maximum value from the business and/or its assets.
You should keep working in the business until such time as you and your partner decide not to sell it as a going concern; otherwise it will lose value as a going concern.
The removal of the Air Conditioner should eliminate the need to apply for a DA, however if you are going to keep it then yes these costs are partnership costs. How this affects your sale price is anyone's guess and is not a legal issue.
Leave issues as to what prospective buyers are told to the receiver. You can get in significant trouble if you are seen to be trying to reduce the interest of prospective buyers in order to secure the property for yourself at a bargain price. Your partner would then be in a position to sue you for damages.
I trust the above assists.
The receiver's first task will be to form a view as to the value of the business as either a going concern or alternately its recoverable value if its underlying assets are sold. If you make it clear you are prepared to pay the higher of those amounts plus $X then his recommendation ought to be that it be sold to you for that price.
You simply have to make sure you stay abreast of what is happening and how he is proposing to liquidate the assets. If instead of trying to maximize the assets the liquidator is being instructed by your partner to simply sell off the components without regard to maximizing the money raised, so as to thwart your efforts to buy the business, you should see a lawyer and takes steps to stop the receiver from doing so.
Yes, the receiver is paid out of the proceeds.
If you make it clear at the outset that you will pay $X more for the business than what the receiver believes he can recover any other way, the receiver should record