The ones I start with - do they all go on the board? The instructions say to place them in the appropriate spaces - just doesn't say what those are.They go on the board. The exact spaces don't matter, organise them in a way that makes sense to you.
And do I have to "build" them or just "discover" them ie explore the land type that is shown on their card? That seems to be how the first one is shown in the rules.You have to build them. To build an item you must have discovered its respective terrain type.
As for those I have to combine - do I lose the item I have to use to use the new invention as happens with the resources?You don't lose the item.
And finally, do I have to build the inventions that come with the characters? As with the explorer - do I have to build the shortcut or just use it when I need it?You have to build them if you want to have them. The character-specific inventions are special only in that:
1) other characters cannot build them and
2) they give the character 2 determination when built.