Your first sentence of your initial post says it all...first year of riding...

It takes time to build the strength and hardness in your legs as well as your lungs, blood system and mindset to become a good climber.

Climbing : To get faster on climbs I need to get into higher gears, but my legs get tired and so I drop into a lower gear and start spinning with a high cadence and then I can't get enough speed. Climbing hills that are more that 1/2 mile result in alternation of low gear spin and high gear off the saddle pedaling.

This is a great opportunity to understand and improve just from the above. Your strength and bodies ability to cope begin to fail and you have to shift into an easier gear and try to spin...this is normal...just understand it is your bodies inability in its' current fitness level. You can improve.

If you can find a hill that is like what you describe, if not that hill itself, you can use it as your building ground and test bed. Hill repeats are best with decent recovery in between each attempt. Twice per week is great. Use landmarks to identify when your body begins to break down and keep a journal of them. As you continue to train you will improve and see those landmarks move further up the hill until you crest it...most important is to continue to pedal over the crest. Many make the mistake of thinking they are done when they hit the crest but not so. It is very important to continue over the crest carrying that momentum with you.

Once you crest the hill you can now continue to improve by using the next higher gear and starting over...there is no completion point merely becoming better and better and how good it feels.

I was not a good climber initially but after several years of hard work I became good enough to do well in some very hard road races in New England...it felt so good to be competitive, whether in a race, group ride or against your previous attempt and it is your hard work that got me and you there.