A couple of simple questions

I'm new to RF design so, a couple of very simple questions...

If I have two or more transmitters, each operating at a separate frequency, can they share the same antenna, all transmitting at the same time?

If I have both a transmitter and a receiver, on separate frequencies, can they both share the same antenna, using it to both transmit and receive at the same time?

Yes that's possible, a mobile phone for example only has a single antenna for transmitting and receiving full duplex simultaneously. The trick is they are using a duplexer for separating both frequency bands.

Yes but you'll have to combine both transmitter signals somehow before the antenna. You can do this before the power amplifier, but then you are likely to bounce into problems with intermodulation. Or you can do it after the power amplifier, but the coupler/combiner will cause some power loss which you definitely do not want. The third way is to do it with a duplexer, this will cause the lowest loss but it is the hardest and most expensive design.