Mike,
Local ripples are almost certainly delamination and restretching will not solve the problem, as the top fabric of the carpet has separated from the secondary backing. When a fitter stretches a carpet, its the secondary backing that he is trying to stretch, not the top fabric. Attempting to stretch the top fabric will make the situation worse.
Only stick the tile down if the rest of them are. Often they are completely loose laid. If you must stick it, use a bit of copydex or other latex adhesive, only a few light blobs will do. Avoid spray adhesive as it may over soften any bitumen tile backing and bring brown stains to its surface.
Cut the tile with a Stanley knife or similar. Simply scribe a line on the tile backing,
with the blade where it needs cutting and bend, so as to crack the back. Then just re run the blade along the line to cut through, and position.
Dave.