I have ambiopia due to prescription difference (hyperopia) I don't have cross eyes or "roaming" eye. Is my child likely to get the same thing?

Not necessarily. Amblyopia is not itself hereditary but the factors which can cause it can be. In other words, your children may not get amblyopia but they are more likely to have a difference in prescription between the two eyes (anisometropia). Take your children to see an eye doctor at 6 months of age and again and 3 years of age. This way, any problems can be corrected in time to prevent amblyopia.
Possible. Ambliopia occurs when the brain decides to turn off the input of one eye if the image is distorted (less sharp, wrong direction, etc.).If recognized early enough, the input can be corrected & vision loss avoided. There are tools like the suresight that can passively pick up different refractive strength in pre verbal kids. With the hx , i'd have your kid screened yearly for early detection if present.