I have chose to do Alcjhemy, Archery, light armor, sneak, and illusion. Possibly one handed as well. My question is, when I am facing dragons, will this build be difficult?

Archery works well against dragons, see no problems here.

Thanks. What about general close combat. I guess kiting will be my best bet right?

You'll be set. Use poisons on Dragons. Remember that Illusion doesn't work on them.

I would actually delay the MQ until you have those skills pretty high, otherwise it'll only lead to frustration.

Yes, and Elemental/Magic Resistance and Fortify Marksman potions.

Your all set your bow can damage them at range while your magic, poisons and melee weapons will wreak havoc on them at close range. But as stated before postpone the Main Story until you can level up your skills otherwise you will get killed a lot and you'll get really frustrated but once your level for each skill tree is around 30 or 50 you should be good to go. Hope this helped.

Sincerely,

Prizrak

I found in my experience that an assasin character is hard to play as in the beginning but as you progress it becomes a lot of fun!

The bow will become your dragon-killing tool since daggers usually aren't that great of an idea against them, although I did 1-hit-KO a sleeping dragon by dual power attack sneak dagger strike with the 15x damage perk and the perks that increase power attacks, plus my one handed armsman perk was 5/5 and I believe I had gloves on that made one handed attacks 25% stronger. A little overkill but it was pretty sweet