do I put a delay between writing and reading of a IOAPIC register

No.

The CPU is already many times faster than the I/O bus, so any short delay you might try to insert would have no affect anyway.

The I/O bus takes care of all the timing. Don't worry about it. The hardware knows what it is doing. You don't need to do anything software-wise to make it work.

no delay is ever needed when writing using mmio/pio.
if hardware needs time to do something and return in other register, it must provide away for you to poll it or trigger irq on completion.
In case of polling, for example you write to one register, and constantly read second one untill highest bit is 1. When its 1, you reset it (write this register again with msb =0) and assume data is 'correct'. This is just an example. If you must write multiple times something on register, i have bad news, you cant do that. You must use polling method every time. If hardware doesnt support it, it sucks. As far as i remember, PIC initialization require writing 2+ icw one after another to 1 register. This is a bad design as controller might be too slow compared to cpu.

(in advance, sorry for my English, I do my best)

In the case of ioapic, there is nothing to do that.
(like you say.... polling or other ways).
It seems that the hardware (ioapic) did not need delay to react.
(since it gives no way to check this delay)
Having said that, currently, the ioapic is part of Southbridge,
that's maybe why it reacts so quickly to requests from the cpu.