Who is more powerful - Drona or Bhisma?

 Bhishma is an Insect compared to Drona.

Firstly drona was the most Inconsistent warrior in MB (mainly due to his Mildness most times).. There are Instances Where he mopped the floor with Arjuna and also Instances where A weakling like Yudhisthira mopped the floor with Drona.

Drona's True Potential can be seen on 15th day , 4 days of failure in capturing Yudhisthira in addition to Duryodhana's insults. He was totally Frustrated and angry on 15th day and went all out. None could stand before him that day.

On 9th day (Bhism's prime), Krishna knew Arjuna could easily defeat and subjugate Bhism but due to the latter's mildness , he didn't did so. So Krishna took up weapons to force Arjuna to fight vigorously.

But this was Krishna's reaction on seeing Drona's wrath on 15th day.

Meanwhile, O monarch, Govinda, knowing that Drona, that foremost of warriors, was capable of sweeping all the Pandavas off the face of the earth, became much distressed. Addressing Yudhishthira he said, 'If Drona fighteth, filled with rage, for even half-a-day, I tell thee truly, thy army will then be annihilated. Save us, then, from Drona. under such circumstances, falsehood is better than truth. By telling an untruth for saving a life, one is not touched by sin. There is no sin in untruth spoken unto women, or in marriages, or for saving king, or for rescuing a Brahmana.'

Because he knew Arjuna cant Even scratch him on that day. Drona didn't had any boon yet Pandavas had to use a Disgusting Trick to put him down.

Beholding the sons of Kunti afflicted with the shafts of Drona and inspired with fear, Kesava, endued with great intelligence and, devoted to their welfare, addressed Arjuna and said, 'This foremost of all bowmen is incapable of being ever vanquished by force in battle, by the very gods with Vasava at their head. When, however, he lays aside his weapons, he becomes capable of being slain on the field even by human beings. Casting aside virtue, ye sons of Pandu, adopt now some contrivance for gaining the victory, so that Drona of the golden car may not slay us all in battle. Upon the full of (his son) Aswatthaman he will cease to fight, I think. Let sonic man, therefore, tell him that Aswatthaman, hath been slain in battle.'

Why didn't Krishna asked Arjuna fight vigorously like in case of Bhishm? Because he was already giving his best and Krishna knew that's the only way to get rid of Drona for Good.

The concern caused by Bhishma was nowhere near What Drona caused.

In this form (15th day) Drona would Eat 1000s of Bhismas Effortlessly.

Bhisma’s best weapon Is Brahmastra whereas Drona posesed pashupatastra, Brahmastra, Narayanastra and Brahmashira. Bhishma Also couldn't do much against Arjuna during his lifetime. Whereas Drona convincingly defeated him on 14th day..

Was Karna trained by Drona as Pandavas & Kauravas?

Radheya Karna was a student of Dronacharya and he used to study with Kauravas, Pandavas, Princes of Vrishnis and Andhakas in his Gurukula. He was extremely jealous of Arjuna and did friendship with Duryodhana and used to mock Pandavas. When he saw Arjuna getting appreciation and becoming better than him, he went to Drona to teach him Brahmastra which he taught only to Ashwathama and Arjuna. Seeing his bad intentions for Arjuna he rejected to teach him Brahmastra. Then he left the school of Dronacharya and went to Parshuram where he lied about his identity so whatever he was taught was wasted as Parshuram cursed him for lying and said he would forget his knowledge when he would need it the most.

Karna was indeed trained with Kauravas and Pandavas in Gurukula of Dronacharya. In TV serials, all the mocking and bad behaviour done by Karna in Gurukula towards Arjuna is given to Ashwathama when he never mocked anyone.