That engine has been severely neglected. Cracked coolant reservoirs and white smoke indicates your A3 may have a blown head gasket.The oil is old too. The crack in the coolant bottle means gas pressures from the engine has escaped into your coolant system and it was so great it cracked the coolant reservoir tank.
If you want to keep the car and save it that's up to you but be aware that repairs to a blown headgasket may be relatively expensive. Ask a mechanic to perform a compression test and a leakdown test on the motor. If the compression numbers are healthy, then the motor can be saved. A leakdown test will verify if your head gasket is blown and will tell you where the leak is coming from. Also if you do have to replace the gasket, ask the shop to check if your cylinder head is warped. If it is you will have to send it to a machine shop.
Now, this all could be not too bad perhaps there is no gasket leak. Perhaps the crack on the fluid reservoir tank is superficial and you need only a new reservoir. And perhaps the white smoke is from bad injectors or glow plugs. There's really no way to tell unless the shop does a compression/leakdown/coolant combustion gas leak test.
But with white smoke, a cracked reservoir, and murky/gunky oil (this means water has mixed with the oil). These are all indicators that it is very likely a blown head gasket.