Can you not also use adjectives and nouns with this construction?
For example:
げんきじゃなくてもいい あつくなくてもいい ともだちじゃなくてもいい
Also the form here is listed with a title of なくてもよい, but the meaning is listed as なくてもいい, same as the てもいい form. Should we not make the term the same over the whole grammar and make a note that よい is also possible?
Actually, using だ after いい (or any other い-adjective) isn't technically correct (though a Google search will turn up some examples of Japanese people saying it, in the same way native speakers make mistakes in English.) です、でしょう、だろう are all fine, though.
Good question! When used with verbs/actions, they are essentially the same. A couple of notes, though:
1. Based on the awesome book 日本語文型辞典, ことはない is often used to say something that encourages/cheers up the listener (ex. 心配することはない - you don't need to worry)
2. ことはない has a secondary meaning - "There are not times when A" - so "無料で行けることはない" would be something like "There are not/no times when you can go for free."
