Is there a space between the move number and the move algebraic
You leave out when and where, so I'm making some assumptions on my own. One of them is that you are not talking about some well-defined format -- on the simple grounds that all you would need to answer that is to read the specification yourself. Thus, I'm talking of printed matter or near equivalents, intended for human consumption.
Yes, always. While a period is a terminator, it is not enough of a visual separator on its own: it needs additional space. However, if you already have the space, you may be able to do without the period itself. (By space I mean any horizontal space: from hair space to em space and beyond. In this particular case, an en space or wider seems required, though.)
In other words, which of these is the correct notation? :
1.e4 e5 or 1. e4 e5 ?
26.Nxe4 or 26. Nxe4 ?
In both cases, the second of the two alternatives. Note however, that using a full space may be excessive. A number space might be enough.
8...Bb4+ or 8... Bb4+ ?
Neither. An ellipsis always stands on its own. It doesn't terminate anything.
The correct format would be
- ... Bb4+ or 8 ... Bb4+
provided that the space between 8 and ... is of sufficient width to clearly separate the two. (Here is where I begin to suspect that you may be leaning against PGN, which has nothing to do with typography, and should not be assumed to do so.)
This does not change if you use another notation than algebraic.
I pick up "Fischer v. Spassky, Reykjavik 1972", which does moves as follows (approximately):
1. Kt-KB3 Kt-KB3
2. P-B4 P-KKt3
3. ... B-Kt3
(White's moves are right-adjusted, Black's move left adjusted. The space allocated for White's move is predefined, as I can find one minor catastrophe when the space disappears entirely:
I would like to know if the designer is happy with that. I see no reason to believe he is. (Added: ... although, ... it might be the best of two poor choices.)
I've seen both with and without the space. On Wikipedia there are
spaces. But I checked in three of my books and there isn't any space
in any of them.
Without space might be an simple but ill-advised way for an amateur to avoid a word processor to split a line between the move number and the move. Or it may be an assumption that PGN move format for some reason is suitable for typographical rendition -- which it isn't However, for PGN your questions can be answered ... but then of course, as per my assumptions above, if the context was PGN, you would have turned to the PGN standard for your answer.