How easy/difficult is it to get companies based outside India to come and demo their equipment before deciding to purchase them? (& what about repair issues?)
It's possible and improving each year. Historically, certain companies have had a strong presence in India, but in general it is possible to get practically any company/their agent to demo a device. One can also visit the company (eg. visiting Zeiss if one is in a meeting in the area) or have them come to India. The latter scenario takes longer, and because of import/export constraints, demo equipment that the company sends to India is rarely re-exported out. So the company makes arrangements to demo the piece at multiple institutions, then offers it at a "demo" rate to one of them.
A new approach to this is that an Institution can have what are company sponsored facilities where the Institution provides the space and pay the import duty but equipment is in the Institution for use. The company also provides a person to maintain the instruments and pays part of the instrument consumable. Such equipment are up for sale at any time of the contract by the investigator for a lower price. Buying demo equipment is also good because you know someone has tested it out and its okay. You can also demo the 'demo equipment'. Several imaging facilities allow other institutional investigators access to them at nominal costs.
With respect to repair issues, all the large suppliers have engineers in India or the Asia-Pacific and will be able to get to you fairly speedily. For very unusual equipment, you might encounter a problem is with a company that insists that it will not provide service onsite after you buy the device, but where you have to ship it back to them outside India for fixing-this is problematic because of customs rules.
Service contracts are fairly expensive. Generally it is worthwhile taking the time to do the negotiations and meeting the service Engineer before you decide on the make/model. Even if you are very familiar and like high-end equipment made by company A but they don't have a good presence in India, its better to go with equally good but not your favorite B. For high end equipment such as an EM, they will often provide an operator.