To get implants how much space is need between teeth and roots?

Minimum of 1.5 mm space is needed between implant and root of a tooth. This is to ensure presence of adequate bone to prevent bone loss. Also prevents  damage to root of the tooth. Safe to have 2 mm. Depending on experience of the surgeon.  

Although dental
implants do encourage natural bone formation, there needs to be enough space
between them and otherwise healthy teeth so that the stability of the implant
or tooth is not compromised. The more space between the implant and the tooth,
the better. You may want to ask your dentist about bone grafting if bone height
is inadequate in other areas.

generally 3mm ideal. 1mm near apex can work. So a 4.3 mm implant would ideally like 8-10 mm between two tooth roots