1) It is not clear what states gave railroads the power to seize property. It is clear that eminent domain has been used to take land for railroads in every state. However, not every railroad had the power to take land; some governments took the property and then gave it to the railroad.
2) No, railroads didn’t have to use easements because they got to use eminent domain. Railroads had to use easements for the same reason they got to use eminent domain – they were using their property to serve the “public interest”. As a result, they got various subsidies and special deals. In return, they were subject to heightened government control. That control included not always having fee simple ownership of their land.
Here are some details:
1) Like many private businesses – from grain mills to canals to shopping malls and hotels – railroads got some of their land via eminent domain. Who could take the land, and under what conditions and restrictions, varied from state to state (and over time).
Unfortunately, as far as I know, there is no list online telling which states gave which powers to railroads. There may be such a list in one of the treatises on eminent domain, such as Nichols' "The Law of Eminent Domain," or on railroad law. (By their nature, treatises are exhaustive.)
However, there is enough information online that you could make a fairly complete list in a few hours; my search for railroad+eminent+domain+(state name) got plenty of hits for every state I tried, including Hawai'i.
Recent changes to state laws show how much state laws vary. In response to the Supreme Court’s decision in Kelo v. City of New London, many states made it harder to use eminent domain for development projects. Some of states (South Dakota) explicitly target railroads, while others (Vermont) explicitly exempt railroads.
2) It’s an oversimplification to say railroads either: a) own their land outright (ie, fee simple); or, b) have an easement. Railroads use other forms of property, including fee-simple with conditions and licenses. What these forms of property share is reduced railroad control over its property. As mentioned above, the reason is simple. To encourage railroads to serve the public, they got subsidies. In return, their rights over their property was attenuated. Thus, railroads couldn't set rates at will. One of the valuable rights they gave up was the right to sell the property once they were no longer using it for railroading.
3) The issues of eminent domain and ownership of railroad rights of way are not merely of academic interest. For example, many people today are interested in what to do with abandoned rail rights of way. Who gets the land, under what conditions, and at what price? Can the land be sold outright, “railbanked,” (using it in ways that allow an easy conversion back to rail in the future), turned into trails, utility rights of way, and so on. Not surprisingly, advocates for each of these uses argues that their use is most consistent with existing rights.
The growing interest in high speed rail raises again the issue of how to get the land for rail projects.
For a nice short summary of the history of railroad rights to rights of way, you might look at Sec I of, Danaya Wright, “Doing a Double Take: Rail-Trail Takings Litigation in the Post-Brandt Trust Era” Vermont Law Review, 2015. There are many good references in her footnotes.