I'm afraid that would be too much to hope for. 
I've never been to the beach, but it depends what you mean by off road. I've taken it across (bumpy) grass fields and so on without any problems. (DS used only to sleep in it if he was being jolted within an inch of his life.) We do a lot of trips down a disused railway line which is part tarmac, part track/mud/random surfaces. I've not had any problems with that.
Obviously it's harder work on difficult terrain. I rarely bother locking the front wheel in position though, and I reckon having that fixed would make bumpy surfaces easier to negotiate.
One advantage of the wheels IMO is the air-filled foam tyres. From what friends with other pushchairs tell me, air-filled tyres are much better than solid ones, but punctures are often an issue with normal tyres. I don't know how unique this is to Teutonia, though.
On less than a handful of occasions I've had problems with tipping - usually when going down a steep hill with a very steep sideways camber too, and with heavy bags swinging off the handlebars and/or back of the pushchair. I think that's just a function of a 3-wheeler though.
Looking at the instructions one day, I realised that at least once or twice a week I load the basket to more than double its recommended carrying weight.
I do all my shopping on foot.
You'll probably find you need to buy a raincover after a bit as the one that comes with it is a bit cheap & nasty (ours tore after about 10 months). I got an 'apron' to go over the seat too, which has been useful.
I do find it annoying trying to put stuff in the basket when it's reclined flat. It'd also be better if you could remove the insect netting completely in the winter, and I occasionally have problems with the brake sticking, although that seems to have improved. One of the clips that made it easier to add/remove the carrycot broke but we had the whole chassis replaced under guarantee.
If you do decide to get one, I'd really recommend getting one with a handbrake if you can. I nearly didn't, but it's been brilliant for slowing it down on steep hills (and there are plenty of them near me).
HTH