Transport from Madrid to SJPDP

I will try to answer you in a few words
1. If I have to catch a train to Pamplona and then a bus to SJPDP is the train station and bus station in close proximity in Pamplona?
The train station is about 4 Km far from the bus station. So you must take a bus or a taxi.

2. Is a bus all of the way possible? If so where is the bus station in Madrid?
You have some bus companies that depart directly from Madrid airport, I think from T-4, see PLM, ALSA or CONDA companies It takes about 4 hours. The best option.

3. Is there anyone else travelling from Pamplona to St Jean the same day. I have had an email from transporte.peregrinos@gmail.com (Ivan) who said he can transport me but at 100 Euro for just me it is too cost prohibitive.
I think its difficult to do all in the same day, dependes of the time arrival at Pamplona. See AUTOCARES ARTIEDA will take you to Roncesvalles. There pilgrims form groups to share a Taxi to St Jean.