Is it possible to demolish one of the rail tracks in a station, and not all of them

Assuming you don't want to break the station in to separate stations and use a load of feeder links, you will need to tweak the advanced option that limits your maximum station spread.

This advanced setting (specifically Stations→Max station spread) can be adjusted to values between 4 and 64, with a default of 12, and determines the maximum size square that can be allowed to bound each station (whether compound or not).

The recommendation is to only increase this if you are using the YAPF pathfinder, but this is the default so if you've never tweaked that setting there's no need to worry.

For more information, you can see the wiki entries for the setting and station spread.

If you need a station larger than 64 by 64, well then I think you're stuck (and possibly doing it wrong).

One-way signals reserve a signal block between it and the next signal.

One-way path signals reserve an individual path between it and the next signal. This allows 2 trains to be on the same signal block at the same time, so long as they have paths that don't cross.

From the wiki:

The two new signal types behave a bit differently than standard OpenTTD signal types. The Path signals are red by default, and will only show green as soon as a train can reserve a path to the next safe waiting position on its route. Safe waiting positions are - by definition - in front of signals, depots and track ends. The back of a Path signal is not considered a safe waiting position, and therefore paths are reserved through these signals.

Because the front of every signal is defined as a safe waiting position, you would normally not want to place a signal immediately behind a junction, only in front of a junction. This is because it is only safe for a train to wait in front of a junction. It is not safe for a a train to wait at a signal immediately after a junction before the whole train has cleared the junction, as it would be blocking the junction while waiting, as illustrated in the example below. This is a major advantage against standard OpenTTD signals, where you had to place signals before and after junctions, which caused trains to block junctions while waiting.

For straight track and basic merges/splits, I stick to normal one-way signals. I use path signals for forks that have 4 or more tracks, as this is where they start to benefit.

Path signals also can behave similar to entry/exit signals, although entry/exit signals have uses that path can't fully achieve. For instance, entry/exit signals will cause trains to take longer routes if a path is blocked, while path signals may wait. This can be used to construct balancers and other helpful constructs.