I don't get the bit about maneuvering at right angles. Allowing one's ship to be raked - the enemy firing down the length of the ship from ahead or astern - was a disadvantage that commanders sought to avoid. Solid shot - most of what the Confederates would be firing - would smash up people, guns, or whatever until it expended all its energy, while the ship's own broadside guns would be useless. A ship end-on would present a narrow target in azimuth but a longer one in range.
Even in April 1861, there were multiple Confederate batteries around the harbor, so a ship could not be at right angles to all of them. Also, a ship's orientation would be largely determined by the channel it had to follow, particularly for a large, powerful warship.
As JohnD mentioned, many of our ships were overseas or laid up in ordinary; the latter included the most powerful, Merrimack's four sisters, which were recommissioned between May 2 and June 20. Ships were able to overcome Confederate forts at Hatteras, Port Royal, etc.; but Sumter was a particularly challenging situation, being inside the harbor, surrounded by rebel batteries. Again, navigating the harbor or maneuvering to engage the batteries would be difficult.
As thomas said, the goal was not to rescue the garrison; the Confederates would have been delighted to let them go! If the fort was successfully reinforced/resupplied, it would still be subject to bombardment. The rebels would repair and reinforce their batteries, and the Federals would have to repeat the mission as long as they wished to hold the fort. In the long term, they would probably have to assemble and land an army to reduce at least some of the Confederate positions; even in early 1861 Scott estimated this would take 20,000 troops.