Byte published a high-level summary of the "abandonware" situation in 2001, which answers many of these questions. However, it's dealing with the case where you simply want the company to re-release the software or release it into the public domain. If you intend to license it and resell it, you will definitely need a lawyer to draft up a contract to protect your commercial rights, at some point in the process.
How To Do It
You don't need to be an attorney or work at a software publisher to bring new life to old software anyone can help make it happen. The hardest part is often finding the right person to ask. If the company that published the software has been sold, you'll have to find out who bought it: A little Web research goes a long way here.
Once you find the company, it's time to approach their attorneys. Call the company's main office and ask for the legal department, or write to the company. The person you talk to may not have heard of the software you're referring to, so be ready to provide as many details as possible, including who published it, in what year, and for what platforms.
Also, know what you want: Asking for a license to distribute the software for free on your web site may be reasonable to many publishers. Or perhaps you'd like the publisher to release the software into the public domain an option that will be distasteful to many publishers who are unwilling to completely give up rights to their work, no matter how old. Don't expect an answer right away even once you find a helpful individual, it may take months for them to give you an answer.
To answer your specific queries:
Whom to contact and what purchase options are possible?
You contact whoever owns the copyrights. This can actually be very tricky to track down in the case of some old games, and unfortunately, there is no general way to handle it. In some cases the paper trail may just be buried too deep, and you're SOL. For example, as described in the Byte article, the legal records needed to transfer the rights to MECC's game catalog are apparently gone forever.
Is it possible to obtain source codes, design documents.
How to deal with localizations in other languages, are they to obtain from other companies or do they belong to master publisher?
They're assets like any other. These may have been owned by a different party to begin with; they may have been sold to a different party during liquidation; they may be lost forever.
Some things, like trademarks, may now be owned by entirely unrelated entities. If they're actually using them for their unrelated business, you probably can't get them at all.
How to deal with various platforms, is it terms of contract saying which platforms are allowed to be used if there are several?
What could be the reasonable price for said games in example?
This depends entirely on your negotiating skill. You want to convince the current holders it's worth $0 to them, and that even $1 would be a great move on their part to let you remake the game on all platforms.
Is it possible to pursue owners to release the game as open-source?
Sure. Open source licensing is licensing like any other. If you have the rights, you can do what you want.