1- How powerful was Vegeta against Jheese? Power level wise, how would you estimate the number that appeared on Jheese's scouter when Vegeta taunted him to look at it?
2-Could Vegeta access [against jheese] the same power he showed against 1st form Freeza?
Let's go:
1- That's debatable. First, we have Vegeta post Zenkai showing fear towards the level Goku used against the Ginyus, saying he is the legendary warrior and speculating he might be a SSJ. This implies Vegeta wasn't at that level yet, as he treated Goku like some sort of God:
Then, it's said by Goku that post Zenkai Vegeta is strong enough to take out Jheese. Vegeta confirms with this that Goku realized about the Zenkais:
Later, Vegeta runs from the fight, stating that Goku and Ginyu's capabilities are pretty much the same and that if they kill each other that would be good for him. That leads us to conclude Vegeta is below Goku and Ginyu, at whatever level he estimated for them.
Vegeta, upon hearing that Ginyu possessed Kakarot's power and that such body can reach a power level of 180k+, is pretty nervous, not to mention being pretty scared upon realizing Ginyu is approaching, further implying he still can't handle such level of power:
Yet, right after it Vegeta says he is approaching Super Saiya-jin and that's the reason his strength is so great. After feeling the weight of his blows, Ginyu thinks possessing Vegeta's body will give him the win against guys who were outstripping him in Goku's body, which doesn't make sense if Vegeta were below 180k, which is the power he associed to Goku's true power:
Goku, when back at his body and back to his ability at sensing chi, also says it'll be the end if Ginyu possess Vegeta's body, which further indicates Vegeta is also stronger than whatever level himself showed at Ginyu:
But all of this clashes with Vegeta fearing Ginyu and Goku, or treating Goku like a God, who was only accessing a BP of ~60k.
2- This is also somewhat debatable. Vegeta says to Jheese that he's approaching the SSJ, something he repeats against Freeza:
This is the same thing he says to Freeza, without noting nothing of feeling way stronger after the nap. He says Gohan and Kuririn are steadily raising in power but makes a distinction for himself:
But at the same time, before facing 1st form Freeza, Vegeta has no confidence in taking him without the immortality, going as far as to say he'll just someday defeat Freeza, that is, not something of a foreseeable future. That doesn't make sense considering he showed confidence against 1st form Freeza and a hypothetical 2nd form Freeza, to which he thought wouldn't change this much:
