I bought several red cordylines and all the leaves have gone a slight brown, yellow colour.?

The cordylines do normally lose their older lower leaves as the plant grows taller. However, if all leaves are turning brown it might be a sign of over-watering. Welcome to GOY as well.

How do I know if there are pests on my Cordylines

How do I know that there are pests and if I do how do I treat them.

See if there are any round or oval shaped brown bumpy patches - that's a sign of scale bug. Sometimes - if plants have come from full sun at a nursery and are put into shady spots, they take time to adjust and vice versa. The signs of new growth though sounds encouraging.

Forgot to mention - look for aphids as well. Little blobs of white between the stems and leaves.