Is it safe to park hired 2 wheeler near Goa beaches?

You will be surprised by the amount of two-wheelers on the streets in Goa (and India for that matter) either being driven or parked randomly wherever possible. Moreover you'll be driving a rented vehicle, be it an old moped or an even older Royal Enfield, who usually all look the same and are of little to no commercial value. Now imagine your parked vehicle surrounded by a bunch of other similar looking ones and you'll understand that you shouldn't have to worry about it being stolen since your two-wheeler will have little or no appeal to thieves. To be even more safe make sure you rent a chain/d-lock of some kind and use it to block your vehicle in place.

Of course your mileage may vary. From personal experience, I parked a moped outside a busy club for longer than a week and found it exactly where I left it.

Yes it's safe and there is no issue regarding parking of bikes(two-wheeler) near beaches in Goa, you'll just have to take care that you are not blocking the way/road.

If you're still having doubts about the safety then there are Paid-Parking(hourly basis) areas near the beaches which are way more secure, so you can opt for them as well wherever they're available.