What was going through Vegeta and Piccolo's minds at this moment?

[SIAD]

What was going on in Vegeta's mind when he saw the fight between Piccolo, Gohan and Krillin vs Frieza Fourth Form? I mean before Vegeta revealed that he is the SSJ.

Vegeta showed some concern at that moment when watching that fight, but later he shows great confidence in defeating Frieza. I always found it confusing what was going on in Vegeta's mind.

What was going on in Piccolo's mind when he saw Vegeta finish understanding himself in his Zenkai Final?

Krillin commented that Vegeta should defeat Frieza without any problem, while Krillin agreed, while Piccolo was impressed by seeing Vegeta and Frieza's powers.

What did Piccolo expect from the fight between Vegeta vs Frieza, just before that fight started?

 

[SSJ2]

Vegeta was at the height of his delusion directly after his zenkai. His power up was enormous, but you could tell that he was still doubting himself to be able to beat Freeza. It also took everything he had to keep up with Freeza's movements and save Gohan from the death beams. Vegeta deluded himself into thinking that he had become invincible after becoming a Super Saiyan, but in all likelihood he was probably still a bit short of initial 4th form Freeza's power.