Hi Oscar,
To answer your question, "Yes". This ARM7 can handle this.
However, if your project is anything like projects I work on, it will most
likely have "feature creep", which means you may run out of processing power,
after management and marketing add everything they can think of to the
requirements specification (eventually they will).
I have purchased the development kit for the LPC2478 from FDI, and have found it
to be very capable of performing everything on your list.
(here is a link to see the development kit)
http://www.teamfdi.com/development-tools-kits/products/1/DK-57TS-LPC2478
I also have purchased the LPC1788 development kit, which has the Cortex-M3
processor, and is faster than the LPC2478 ARM7.
(here is a link to see the development kit for the LPC1788)
http://www.teamfdi.com/development-tools-kits/products/1/DK-57VTS-LPC1788
I believe the two parts are about the same price, and I believe the LPC1788 will
be available in production quantities very soon (don't know for sure -
waiting on a response from Gene).
I hope this helps you,
Dave