2005 E53 3.0D Transmission Issues

[jdd]

I had exactly the same issue as your point 1 after I purchased mine a number of years ago. I learnt to adapt my driving style to minimise the effect however; if you do some research on this it is a reasonably common problem. A simple search on Google of the words "ZF lurch" will reveal 100's of results mostly related to various BMW and Jag models that have the ZF 6HP26 auto.
A while back I bit the bullet and had the transmission serviced and the problem has thankfully disappeared. It is a hotly debated topic about whether transmission services on high mileage cars cause more problems than they solve.
I would recommend you take it to a reputable transmission specialist and let them diagnose the issue. BTW, the 6 speed Falcon also uses this same transmission so that may help you decide where to take it.

Edit: Mine now has just turned over 220,000 km and the transmission is still operating perfectly.
Edit2: As the transmission doesn't have a dipstick it is possible it is low in fluid as it is common for these to leak from where the wiring loom goes into the transmission. Not usually a large enough leak to drop anything onto the ground as it collects on the plastic stone guard under the tranny. I had a new style loom & seal fitted to mine at the last service which has stopped this leak. I believe this same leak issue is also common on the Falcons too.
Finally, note that this transmission requires a special fluid which is not readily available (ZF lifeguard 6), and consequently it is rather expensive.