My friend tells me the first action when using experimental interface has to come from the ships action bar and therefore I can't use it to trigger both Expose and Lando. Is this correct?

No.

The extra action from Push the Limit has to come from the action bar. The one from EI has to be an action card. The initial action that triggers either can be any action, bar, upgrade, or damage card.

So you could do Expose > EI > Lando or Focus > EI > Lando.

Or with PTL, Expose > PTL > Focus or Focus > PTL > [another action from your bar].

You could never do Focus > PTL > Expose, nor Expose > EI > Focus.

(In practice the order makes little difference unless one of the actions is a repositioning one or checks range in some way, but it can be important in those cases.)

Nope. Only the action you use after triggering experimental interface needs to come from a card with the action header.

Just for reference, you can trigger your EI even with a free action (i.e. coming from Advanced Sensors or pilot skill).

So could I use PTL to trigger Lando. Roll two defensive dice. See what I got and then choose an action from my bar?

PtL isn't used first. It's triggered after an Action: is taken.

You'd declare the Action: of Lando first and roll accordingly, then trigger PtL off of Lando to declare an Action: from the Action Bar.

Semantics.

So could I use PTL to trigger Lando. Roll two defensive dice. See what I got and then choose an action from my bar?

As Slugrage stated, Push the Limit is triggered after an action is performed. Check the text on the card for the timing.

"Once per round, after you perform an action, you may perform 1 free action shown in your action bar. Then receive 1 stress token."

So, you can only PtL once during a round, and that's after some other action (from an Action: header card OR your ship's action bar), and when you've completed that second (action bar) action, you receive a stress token. And the stress token doesn't stop you from performing that second action either, but it will stop any further actions (free or otherwise) later in the round.

Experimental interface is very similar, but only allows an action from Action: header card as the second action, instead of one from your action bar like PtL.

Both Push the Limit and Experimental Interface can be triggered by any action you've just performed; Upgrade card, action bar or critical damage card. So you can tell your friend he's wrong.

You can perform the Lando action, roll your 2 defense dice and add any focus or evade results as tokens, then trigger Push the Limit and perform a focus or evade action (if you have them on your action bar). Assigning any tokens from the Lando action, does not count as performing the evade action or focus action in any way.