In Arkham Horror, if I lose a turn and then am drawn into a gate, am I then only delayed?

Question

I am not sure what 'losing a turn' is. Is it identical to being lost in space and time in that nothing, even monsters, affects you or fights you? Does being sucked into a gate that appears then convert me to simply being delayed?

Edit: Here is some documentation I found in the Dunwich Horror rules which implies that being drawn into a gate nullifies and previous delays and lost turns and 'resets' it in a way while retaining any possible benefits earned for the previous cost/penalty of delay/turn-loss. It likely means the accepted answer's latter section on what to do in these more complicated situations should be modified.

A link to the Dunwich Horror rules (part of interest on page 10)

Q: If an encounter, when failed, tells the investigator he must “stay here for 2 turns and gain 2 Clue tokens” but before the 2 turns have ended a gate appears at the location and draws the investigator into an Other World, does the investigator lose the 2 Clue tokens?

A: No. The investigator immediately receives the Clue tokens when he or she agrees to meet the requirements of the encounter. If a gate opens in the meantime, the investigator is sucked through the gate and becomes delayed in the Other World. He no longer has to miss two turns if sucked through on the first – the new condi- tion (being delayed in the Other World) is in effect.

Answer 1

Losing your turn is different to being delayed. Being delayed means you cannot do anything during your movement phase

If you have lost your turn, you skip all phases (including upkeep) except for the Mythos phase.

From the FAQ:

Q: If a card tells you to “lose your next turn,” does this mean skip all phases, including Upkeep?

A: Yes, all phases except the Mythos Phase. Note that this is different from being told to “stay here next turn,” which means you are delayed.

For your original question, based on the above, I would say you can only get sucked in to the gate that appears as part of the Mythos phase and then you have both lost a turn AND are delayed.

On your next turn, you cannot stand as that normally happens in the movement phase. You also do not have any encounters. The turn after that, you get to stand and have encounters. The following turn will be when you can actually move. This way, you still have at least 2 encounters in the other world (unless you get lucky - but to be in this situation, you need to be really unlucky)