Ok, I'm 98% sure I know the answer to this one, but watching a number of Youtube videos has got me confused.

If a runner runs on R&D say 4 times in a turn she just gets to see the same top card 4 times right?

Unless that card was an agenda in which case she steals it or has something in their rig that allows them to see more.

It is just in a couple of videos I seen the runner access more without noticing if there was anything specific on the board that allowed this.

The Runner may access additional cards IF they have multi-access cards available, such as:

Medium

The Maker's Eye

R&D Interface

Indexing (not strictly accessing, but they will SEE multiple cards)

Also you are correct that if they somehow remove the top card (steal, trash) then they can see more on the next run.

Barring the removal of the top card or a specific multi-access card, then no, additional runs reveal no new information (but may be useful in the case of building board state, such as with Datasucker or Haemorrhage).

You are correct, unless a card is put elsewhere as a result of an access it goes back to where it was, in this case back on top of R&D. If the Runner then made another R&D run he'd access it again.

However, there are several ways to either access multiple cards per run or remove cards you've already seen.

Keyhole also resembles multiple cards being accessed.

Cool, must have missed something on the vids.