Can I convert my home theater surround system to wireless while still maintaining my receiver and speakers?
Possibly, with some conditions, but neither easily nor economically. You would need several hundred (or maybe thousands) of dollars worth of add-ons that could reduce the sound quality and at the same time be points of potential failure. There will Always be situations where wires are the best method, of which a surround-sound system is a prime example.
You can, There are kits sold that can do that, but I don't recommend it. Each "module" is powered, and would need to be plugged in somewhere, so it is not as big an advantage as it might seem at first blush. Usually (almost always) the sound and the size of the miniaturized amplifiers they use to drive the speakers are inferior in quality and power, to the amplfiers built in to the reciever that you already own. It is money spent unwisely for poorer sound, and unless running thin wire is out of the question (which is almost never) not a best choice.
Somewhere between unlikely and absurdly expensive and impossible.
There are Bluetooth receivers that convert to analog (as add-ons to traditional receivers), but I'm not sure which wires you'd like to eliminate.