I'll offer up some opinions on a few of your questions.
1. What are major differences between T series processor T6400 and Pseries 8XXX ...?
If you check out the processor number comparisions web site (http://www.intel.com/Consumer/Learn/Notebook/core2duo-detail.htm#proc-num), you'll see that the T6400 has a higher max TDP (power), has less cache, lower front side bus speed, and lower clock speed than do the P8xxx series processors. What they have in common is that they are all dual core processors and are all manufactured using the 45nm silicon technology.
T6400 - 2.00 GHz, 800 MHz, 2MB cache, 35W max TDP http://ark.intel.com/Product.aspx?id=40479&code=t6400 (VT not supported)
P8800 2.66 GHz, 1066 MHz, 3MB cache, 25W max TDP http://ark.intel.com/Product.aspx?id=40380&code=P8800 (VT supported)
P8700 2.53 GHz, 1066 MHz, 3MB cache, 25W max TDP http://ark.intel.com/Product.aspx?id=37006&code=p8700 (VT supported)
P8600 2.40 GHz, 1066 MHz, 3MB cache, 25W max TDP http://ark.intel.com/Product.aspx?id=40380&code=P8600 (VT supported)
P8400 2 2.26 GHz 1066 MHz 3MB cache, 25W max TDP http://ark.intel.com/Product.aspx?id=40380&code=P8400 (VT supported)
2. From a performence point of view, which one is better...?
Better is relative. If you take a look at the "Intel® Processor Ratings" (http://www.intel.com/consumer/rating.htm), the P8xxx series processors have more stars than the T6xxx series processors. I take this to mean the P8xxx series processors have a better combination of features. Take look at the processor ratings site and decide for yourself which may be better for what you need.
3. Which processor supports many OS like windows, mac and Linux ...do they both support VMware..?
I am pretty sure the T6400 and the P8xxx series processors should all support Windows* and Linux*. For VMware* support, look for a CPU that has the following feature: Intel® Virtualization Technology. You can check the features for each processor by searching for them in http://ark.intel.com/. Check with Apple* for Mac* OS support.
4. Can I use T6400 based laptops for engineering applicatons like graphics and run simulations?
It all depends upon the application and simulation requirements. I think this has more to do with whether you have an integrated or discrete graphics solution. Integrated graphics uses the system CPU and memory whereas discrete graphics typically has it's own dedicated processor and memory.
Intel Customer Support
*Other names and brands may be claimed as the property of others.