Can I use this sign for 'street' or 'road'?
Yes! In ASL, this exact same sign is commonly used to mean 'way', 'street', 'road', or 'path'. The context of your sentence will let the other person know exactly which concept you mean.
Do I always move my hands straight forward?
Usually, yes. However, ASL is a spatial language. If you are telling someone to go a specific way, like taking a winding path or turning right, you can move your parallel hands in that specific direction to show the actual route.
Should my thumbs be tucked in or sticking out?
For a standard flat handshape or 'B' handshape, your thumbs can rest naturally alongside your index fingers or be slightly tucked across your palm. Just make sure your four main fingers are straight and held closely together.