Can a single 'OV-chipkaart' be used for multiple people from Eindhoven to Amsterdam, and then locally in Amsterdam?

You can get anonymous OV-chip cards as well as ones that are bound to a person, with a name and a picture on it.

Both kinds can only be used for one person at the time, the anonymous ones can be used by different people at different times.

For the train you need €20 on your card, for city transport in Amsterdam €4 unless you need to take the train there as well.
At the start of your last train travel you need to have at least €20 on your OV chip card, whether personalized or anonymous.
At the start of the last bus journey you need to have €4 on your card.
Mostly your travel will cost less which will leave you with left credit on your card. You can get it paid back, as far as I know main train stations can arrange it, otherwise you will have to send it in. And as far as I know, you will not get the cost of the card and they keep €2.50, for the service. You can retain the card and it will be good for a travel in the future, but the card will expire 5 years after you buy it.

In your case I would get a one time use card with the train ticket, which is €1 more than when you have a long term OV chip card, or even better, I would buy online and print my own ticket, which costs the same as traveling on a long term OV chip card.
You can buy a same day return ticket, which will cost the same as two one way tickets but with only once the extra cost for the tickets and credit card use but as you want to stay in Amsterdam a few days, you can not use those. So two one way tickets bought online each are likely the best.

In Amsterdam you have the option of buying a one day or a multiple day public transport pass, using an OV-chip card or buying one time card which are basically tickets for 1 hour, how ever many travels you can do within that time, those cost €2.90 each, (2016 price.)

If you are in Amsterdam for just a few days and do not want to do a lot of things which are quite far from each other, I would not get a day or multiple day pass for the public transport, it will be quite easy to walk, do a canal boat tour where you can hop-on and off, and take the odd (one or two) tram rides. If so, just buy them in the tram or bus, it is more expensive but less than buying a €7.50 OV chip card each. This site has all the public transport options for Amsterdam listed. And this site list prices as well. There are too many options to list them all here, in short, if you use the tram or bus less than 3 times each day you will not win much by having a pass. The one exception is when you buy the pass with museums included and you want to visit most or even all of those museums.