At the start of The Fellowship of the Ring Gandalf catches Sam eavesdropping on the conversation between him and Frodo about the true nature of the ring. Then Sam panics and pleas to Frodo:
‘Mr. Frodo, sir!’ cried Sam quaking. ‘Don’t let him hurt me, sir! Don’t let him turn me into anything unnatural! My old dad would take on so. I meant no harm, on my honour, sir!’
Can Gandalf really do such a thing or is Sam just plain enough to believe that wizards are almighty?
We don't really know. Much about the Istari is left unsaid in The Lord of the Rings, and the nature of their powers and abilities is unclear at best.
We do know that Samwise is indeed very simple, or "plain", as you put it. It is not likely, at least in my opinion, that Gandalf could turn Sam into something unnatural. It is absolutely impossible to imagine that he would turn Sam into something unnatural.
As far as actual displays of Gandalf's powers are concerned, we don't see much of this. He glows, at times, scaring off Nazgul. He fights and kills a Balrog, which no one else in the party could have done. He breaks Saruman's staff. He resists the fear of the Witch King, unlike everyone else. He has good relations with the Ents and the Eagles, which is unusual. He takes the untamable Shadowfax. He lifts Theoden out of the shadows of Grima's spell. He has great foresight and wisdom. He "adds some touches of his own" (images of horses and riders) when Elrond creates the flood that washes away the Nazgul.
That's about it, really. Whatever other powers he may have, we don't hear about them.
