Thor's hammer Mjolnir was defined by the fact that only the 'worthy' could lift it – so basically no-one except the god of thunder (and Vision, for some reason). But when it comes to the weapon's replacement, Stormbreaker – which Thor forges in Avengers: Infinity War – Groot is able to lift it too.
Stormbreaker can be used by anyone, it isn't bound by Odin's enchantments to only be lifted by the worthy. Mjolnir is, however, still enchanted, meaning that only those that are worthy may wield it. This applies to your last two questions as well. If you can lift Mjolnir, you can wield it.
How can Groot's arm strong enough for Stormbreaker? The weapon needed a handle, so Groot created one out of his own severed arm to aid in Thor's survival with a new finished weapon. As a result, the handle still contains some remnant parts of Groot, as is shown throughout Thor: Love and Thunder.
The handle of the Thanos-killing magic ax is actually made from the wood of Groot's own arm and the teenage tree had no problem lifting Stormbreaker. However, Stormbreaker has no enchantment placed upon it about worthiness so likely anyone could wield it.
Meanwhile, MCU Phase 4 saw Stormbreaker being wielded by Thor, Gorr the God Butcher, Love, and anyone else who was strong enough to actually lift and swing it. This is because of the respective origins of both legendary Asgardian weapons.
The REAL Reason Why Groot Can Lift Thor's Hammer And The Other Avengers Can't
Can Groot lift Mjolnir?
Thor's hammer Mjolnir was defined by the fact that only the 'worthy' could lift it – so basically no-one except the god of thunder (and Vision, for some reason). But when it comes to the weapon's replacement, Stormbreaker – which Thor forges in Avengers: Infinity War – Groot is able to lift it too.
Stormbreaker has the additional power to summon the Bifröst, allowing Thor to teleport anywhere in the Nine Realms. Screen Rant has identified Stormbreaker as the more powerful of the two, based on this ability, as well as it being a much larger and edged weapon.
Stormbreaker can be used by anyone, it isn't bound by Odin's enchantments to only be lifted by the worthy. Mjolnir is, however, still enchanted, meaning that only those that are worthy may wield it. This applies to your last two questions as well. If you can lift Mjolnir, you can wield it.
Originally Answered: Can Cap and Iron Man lift Stormbreaker now? Yes. Anyone can lift storm breaker. Because Odin did not said that Storm breaker can only be lifted by those who are worthy as he has said to Mjolnir.
To be clear, Stormbreaker was never given the same hex/curse as the hammer was given. So the scene wasn't about him lifting it but about the sacrifice to form the handle.
Groot's abilities are all-natural and stem from the dendronic wood that makes up his entire body. The extraterrestrial bark he was born with makes him invulnerable to most projectiles and even fire. He can control all plant life via psychokinesis, absorbing it into his body and making himself stronger.
It is safe to say that Stormbreaker cannot be destroyed by anything audiences have seen in the MCU so far. A power that Stormbreaker lacks is the "worthiness" enchantment of Odin. Anyone physically strong enough to lift and use Stormbreaker can use it.
Many viewers have pointed out that Thanos was able to lift Stormbreaker without a problem, but this is because the ax isn't enchanted as Mjolnir is. Others believe Thanos lifted Mjolnir (although briefly) and have even argued that he would be worthy of doing so.
There's a chance it could be repaired -- after all, Mjolnir has been broken and remade on multiple occasions -- but seeing Thor break Stormbreaker willingly is still a shocking sight. By destroying Stormbreaker, Thor not only reaffirms how powerful he is, but he also shows Bill how determined he is in his new quest.
MCU Thor cannot fly without Stormbreaker or Mjolnir. The best he can do is jump long distances, which is still dang impressive. Stormbreaker is called the King's weapon in Infinity War.
Thor. Thor, the god of Thunder, was undoubtedly the most powerful member of the original Avengers. His power continues to grow in the Marvel Cinematic Universe.
Overall, though, Stormbreaker seems to have the edge over Mjolnir once again. Strong enough to open the Bifrost, reach Eternity, and manipulate storms the same way Mjolnir can, Stormbreaker's powers are greater than that of the mythical hammer.
Tony Stark was the second one to try, even joking about ruling Asgard if he lifted the hammer and what he would do as king, but his always overly-confident attitude quickly changed when he realized he couldn't lift the hammer.
If Marvel fans have ever wondered if Spider-Man was worthy of lifting Thor's hammer, the answer is yes. Just NOT the Spider-Man you think… Although he didn't really meet Thor beyond a couple shared scenes in Avenger's Endgame, Spider-Man has shown he's actually a big fan of the Thunder God.
Why can the bad guy pick up Stormbreaker? Because unlike mjolnir, Stormbreaker doesn't have any Magical-enchantment on it. It's just heavy and can be lifted by anyone who's physically strong. It doesn't have any special worthy enchantment on it.
Make-believe metal is kind of hard to weigh. But then, in 1991, Marvel released a "Thor's Hammer" trading card that claims that Mjolnir weighs precisely 42.3 pounds. Yet, using the dimensions and weight on Marvel's trading card, it's estimated that the density of Mjolnir is about 2.13 grams per cubic centimeter.
Due to it being composed of Uru, the weapon is nigh-indestructible and able to withstand energy blasts created by the Infinity Stones. It is also able to channel dimensional energy and summon the Bifrost Bridge, which enabled Thor to teleport himself, Rocket Raccoon, and Groot to Wakanda.
He has feats such as defeating Surtur (who can destroy a planet), conquering the 9 realms, and sealing away Hela. While there isn't much doubt that Thanos could beat Odin if he had all 6 stones, Odin could probably defeat Thanos if he only had one or two of them.
Mjolnir doesn't damage Cap's shield at all, as shown below. I think it is fairly safe to assume that Stormbreaker (being a cutting weapon, rather than Mjolnir which is designed to smash or build) would inflict similar damage to the shield as Thanos sword does. Conclusion: Stormbreaker minces Cap's shield.
The answer is that Thor can't beat Superman with his Stormbreaker, of course, his Stormbreaker will provide him extra power and capabilities but winning against Superman is not possible with that Axe. But it can harm Superman because the axe is enchanted and Superman is vulnerable to magic.
