Sentence 1: Great to be back on the TEDx stage. A lot has happened since I've been at TEDx.
When this person said this it was their second time at TEDx, so "I've been" in this sentence is being used to talk about a finished thing. Basically "since I've been" means something like "since the last time I came here at TEDx".
Sentence 2: We've cut taxes about 16 times since I've been in office
Obama said this in 2011, when he was president, so "I've been" is being used to talk about something that started in the past (2009) and was still true when he said that (2011).
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It is "have been". It is basically never correct to say "am been", and it wouldn't mean what you want it to mean anyway.
One possible, correct sentence is:
I have been, for a short time, an employee of that company.
Or (this is more natural for me, but arguably less correct):
I have, for a short time, been an employee of that company.
Either way, it means the same. It says that you were employed a short time ago. It doesn't mean you're about to leave. I see why you might want "from" in this case, and not "for", but don't panic: in this case, "for" does not mean that it will only be "for a short time"! Just that it is "a short time" so far.
Now, you said you didn't want a grammatical or technical explanation, so we can stop there. But in case anyone else wants to know the grammar behind it, I'd like to elaborate a bit anyway.
A construction like "have been" is called the present perfect. It is for actions that are past and finished, at this moment. Its structure is have + past participle.
(There is also a past perfect, which is for actions that were already past and finished at some previous time. Its structure is had + past participle.)
A construction like "am being" is called the present continuous. It is for actions that are happening (right now), or that often happen (not necessarily right now, but before now and, we expect, after now too). Its structure is be + present participle.
But "to be" leads a complex existence. It is also used in ways that are basically unrelated to the present continuous.
A construction like "am been" is called the present passive. It is for actions where the subject ("I", in "I am been") is the recipient or target of the action. Its structure is be + past participle. You might say "I am insulted" (someone gave you an insult), or "I am seen" (someone saw you), or "I am blessed" (someone gave you a blessing).
It would be very unusual to say "I am been", though. That would mean someone was being you. If an English speaker really wanted to say that, they would almost certainly use different words.
“I have been, for a short time, an employee of the company” is a technically correct way to say the you are still working at the company, but started there only recently. I have been is used for an action started in the past, but not yet ended. It would be more natural to say “I have been an employee of the company for a short time”.
“I had been” is used for an action started in the past, carried out for a period of time, then stopped. But “I had been an employee” says you are not longer working there.
“I am been” is wrong. “I am being” is usually used for an action happening at this moment. “I am being employed at the company” would mean that you were, at this moment, starting employment there, or being offered employment there. You’d be more likely to use it with a more active verb, like “I am being chased by a bear!”