The school must be way behind if they only have Pub 97.
Do they have a PTA, if so you could try to persuade them to all chip in and come up to date with Pub 2003. Misco have it in stock at £77.84, surely that can't be beyond the school budget?
Q3. Anything created on an earlier version can be read by a later version but not the other way round. Anything created on Pub 2003 can't be read by Pub 97 and I would think the same to apply with Pub 98.
Q2. Possibly, providing you specify where you want it installed as opposed to the standard "C:\program files."
Q1. I don't have XP so I can't answer that, sorry.
Most schools will be running networks, extensive networks in secondary schools. One copy of a program will be of little use - a site licence is needed. Schools get quite a good deal on these but they are still not cheap.
If you need to transfer to an older version you need to use the 'Save As' option and save it as an older format - though from memory it only offers as far back as Publisher '98.