I'm 5'7" and a short-legged knuckle-dragger. I have 170s on my single bikes and a 175 on the tandem. The 175 works, but definitely slows me down a couple RPM. So I'd say the 175s are fine. 175s are proportionally much shorter for you than my 170s are for me. You could go longer.
Yes, so build up to it. Might take a couple years. Don't be impatient. You wanna be smooth and efficient - this is a great way to get there. You might start out at only 105, but you'll be surprised how you'll get better if you ride a lot. Start with this: 15 minutes of zone 1, 15 minutes of FastPedal, 15 minutes of zone 1. Next week do 20 minutes of FastPedal and the same zone 1. Etc. Only do it on rollers - it's too easy outdoors.