One can wear the Tulasi garland offered to Perumal and do the rituals, but it is not in practise to wear the entire day.
It should not be worn during alpa shankai and asaucam period.
One can wear it separately but not permanently. There are two types of garlands – one is made of Tulasi leaves and another one is made of Tulasi beads. Garland made out of dried Tulasi beads are used while performing austerities and not garland made out of leaves. Not sure what is your question about.
Tulasi bead garland can be worn along with lotus bead garland or can be worn separately also, it should be pure; during taints (asaucam and theetu) it should not be used. While travelling it should be avoided as we might come in contact with taints.